The answer is NOT $1.50. Because if you said the cost of the book was $1.50 then you had already assumed that the cost was $1.00 and that is a contradiction.
But you changed the question! The answer is actually unsolvable because the original question has cost AND PRICE. You can't just change an entire word (variable) and act like it's the same sentence. I'd take this one down. It's wrong on a few levels. And there was a multiple choice answer for "I don't know" which is actually the right answer. You're wrong like 96% of the respondents.
@@duckheadbob I did change the word, not the question. The cost and price mean the same here from a consumer’s point of view. It’s like a ticket costs you $5 is the same as the price of the ticket is $5. I should have emphasized this a bit in the video tho.
@@bprpmathbasicsnope. A cost is an Incurred amount of a product. The price is what a business sells it for. A bookstore buys books at a COST and then sells them at a marked-up PRICE. That's how they make money, these are basic business terms and they mean different things. You again are ASSUMING the pov of a consumer and not the owner. Was there a sentence than claims you're a consumer here? Nope? Well then... And even if you want to look at it that way, you need to SHOW YOUR WORK and declare price = cost = X .... you did not do this. This is wrong dude. Why would the multiple choice option have " I don't know" then? Because that's actually the right answer as price =/= cost. I'm literally doing a budgeting spreadsheet right now, our COST to do this service is not the same as the PRICE we are charging the client. This is wrong. I'd suggest you take it down and redo it.
@@duckheadbobI understand what you said and I did say that I should have mentioned the cost is the same as price in my previous comment. However the answer to the original post is $2. You can see the description for the link to the original post. Cheers.
@@bprpmathbasics again NO. The answer to YOUR question is 2.... the answer to the original question is the multiple choice answer "I don't know." The equation is X = 1 + 0.5y. you do not have the information needed to solve so you do not know the answer. Like cmon dude. This is flat out wrong. I looked at the post and there are others answering the same way I did. You're doing and perpetuating bad math here my man. The FACT the equation has made the distinction between cost and price by using two separate words is expressly indicating you need to declare them as two variables. There is literally an answer in multiple choice that expressly relates to this *correct* line of thinking. It's okay to be wrong, but you need to admit it and not just hand-wave away the correct answer and point me to the oringal post where TONS of people are giving the same answer as I am....... Bad teaching moment. You're unironically trying to use English synonyms to declare values are equal in a math equation - this is nonsensical and not how logical mathematics works at all.
Also there is a HUGE assumption that "cost" = X AND "price" also = X..... that's not a given. This is wrong mathematically as well. If you want to make it into an equation you can't just go cost = price so they both equal X. 2 as an answer would work if the question was: "a book costs 1$ plus half its COST. How much does it cost" Having price in there instead of cost is an indicator it's a different variable. So the actual equation is X = 1 + 0.5Y - which is unsolvable without additional information. Noticed how he changed the language of the problem to avoid this?
This is such a great comment! I write software as a job, which in essence is creating semantics to help describe what the software is doing. When I first looked at the problem, I instantly realized that its description was not very clear and should have been better written.
No... People would still take the added sales tax route... Cost = what you spend = price + tax and or other fees, price = listed portion of cost = $1, tax/extra fees = half of price = 50 c, therefore Cost = $1 + 50c = $1.50
I think if they word it like that then it would have been a different question, I think how they worded the question is right if the answer was going be to 2.
I have the impression that this "math problem" was phrased confusingly on purpose to create maximum engagement when posted as a "problem" on social media.
Unfortunately this is pretty common practice in any standardized testing. I had a math teacher spend nearly a full week just on prepping us for the needlessly confusing word problems portion of the state standardized testing being used that year.
@@jamesbumgardner1469 I'm not from the US so I wonder whether that is on purpose. If so, that would be disappointing. I mean, having a challenging math problem is one thing but having it be a challenge because you aren't sure how to even parse the question seems counterproductive to me. And seems a surefire way to kill interest for math in many students. 😕
@@jensraab2902Yes it seems to be a game to them, are they teaching semantics, English or math it should be teaching math not a mess of gibberish. Like people said in this comment section as a whole, cost and price can mean the same thing for laymen or in finance different things. A.k.a. the problem is a joke from the start.
@@jensraab2902 People that have to have things laid out for them in a certain order, people that can't handle 2 problems at once, people that can't handle 2 DIFFERENT types of problems at once, do you know what those people have to say about that? "Would you like fries with that, ma'am?" People that can tackle and correctly solve multi-part meant-to-confuse problems are airline pilots, engineers, etc. Coddling people does them no good.
I've always hated these "problems" because its an understanding of english issue more than it is a math problem. Its literally just a mind game before you even start doing the math.
Or it’s just teaching you to do basic algebra, I did tons of these sort of questions as a kid and they are probably the only part of mathematics that will actually be useful in everyday life because turning English sentences into algebraic equations is surprisingly useful.
@@imadeanaccounttocomment7800 The math is the easy part here though, this wasn’t a hard equation for most ppl because of the math. It was because it was poorly worded English.
The sentence is worded fine. The content creator just misunderstood the sentence and wrote the wrong formula for the word problem. There is only one correct way to read the original sentence, per proper English. "Plus half of its cost" is a prepositional phrase that modifies the direct object "dollar" ("one" is its adjective). The book costs one dollar. What an individual would actually end up paying for it is $1.50.
@@JeremyB8419 that doesn't track. In the same sentence you are saying that the book cost $1 and that the book cost $1.50 . Although 1 if different than 1.50. You can't have the book both cost $1 and $1.50. the only way to read the problem was the cost of the book = 1 + (the cost of the book) / 2
What i have finally realised through my years of studying maths is that the question will always be a word question which is poorly worded if it is to be challenging and tough because... Math is hard because they make it hard, it is pretty simple actually.
This was really clearly worded though. The trick is to think about it the same way you would a more complicated problem instead of just jumping to the first thing you think and calling it a day.
@rs180216 Cost and price can refer to different things, which breaks the problem. It's poorly worded in its original form, though the wording in this video is fine.
@@rs180216 Not really, the statement is pretty ambiguous to set people up unfairly. Majority of the people took "costs" as them telling us that 1+0.5x was the cost and x was unknown and that`d be right because no one is going to assume that the whole equation is = x as that would mean ignoring the latter half of the sentence and basic reading skills tell us that`s wrong, I`d say he worded it better but also changed th queston a bit so a value could be obtained, no an expression.
The REAL way to word this is to put it in a frame of reference with language people actually use. "You buy a book at the store. The price of the book was $1 plus one half of the total amount you spent on the book. How much money did you spend on the book?" This way of writing it is both concise and intuitive.
Fairly certain this word problem is needlessly complicated. The trickery is in the semantics of language, not the algebra. Different people read different meanings. The people getting a $1.50 are reading this problem as if the "1/2 it's cost" is a tax, in which case they are correct. They read the cost as previously defined.
The most accurate interpretation of the original problem is that the $1 is a flat fee and the "plus half the price" is a 50% discount. A much better way to phrase it would have been: "A book is half-off plus $1. What does it cost you?" The fact that it is unsolvable would have been much more clear, though I'm sure that someone could still find a way to rephrase the question in a way that perverts its meaning to fit whatever answer they want.
No I think people are interpreting as, "a book costs 1$..... Plus half it's cost" sort of like it's two sentences. So in the first sentence the book's cost is already established.
In the second case, there're not enough conditions for this sentence to be considered as a completed math problem, the only real answer is 1+x/2 where x is any number higher than 0, everything else works on assumptions that aren't in the sentence. So laughably the solution in the video is a wrong one, unlike the 1.5$ one, which is one of the two possible solutions. 😂
The overwhelming majority of the English-speaking population would consider the answer to be $1.50, based upon the semantics. That makes $1.50 the answer. That's how language works. The issue isn't people getting a math problem right or wrong. The issue is with people getting basic English wrong. In his replies, the video maker states that "cost" and "price" mean the same thing, so he simply changed "cost" to "price". Normally, one would read the sentence and take the usage of two different, yet similar, words to imply a distinction between the two. The video maker, however, kept the original sentence in the thumbnail, then proceeded to equivocate the two terms into a singular one, and solve a math problem that wasn't present in the original. This is an Equivocation Fallacy, which is also sometimes called a "bait and switch" fallacy. He literally clickbaited people and then told them they were wrong, because he changed the question after people already answered it. If his English is just genuinely bad, and he just made an honest mistake, well then that's just on him.
When I was very young, in the 4 or 5th grade, and I had problems like that in school, my dad told me: "Just call the thing you are supposed to find X. Then do the calculations as usual". I was puzzled: "Can you do arithmetic with letters?" He said: "Sure, just try it". I have used this method ever since, it never fails, lol. PS: The teacher said, "you cannot solve it this way, we are not supposed to learn about using letters in arithmetic until the 7th grade."
Except if you got 2 here you'd be failing your own rule as you didn't make cost = c and price = x There are two distinct words here, thus you need two distinct variables. The answer is "I don't know"
@@TheHappyZappyprice is how much you pay while cost is how much the store pays to get it ( or vice-versa can't rember but price and cost do mean different things )
@@calebkaminski6951 But it’s all in relation to the person being asked a question, being asked the “cost” of your dinner or the “price” of your dinner are equivalent. No one would consider what the restaurant payed for your meal. They are synonyms.
I remember someone saying that these are like saying "I saw a man with a telescope" and having to assume if the man he saw had a telescope with him or if he saw the man using a telescope.
If we then learn that he saw a man using a telescope it creates another possibility; did he see the man using a telescope or was he using a telescope and saw a man. English is the perfect language for unsolvable riddles with such ambiguities.
@@Aetius_of_Astora yeah, english is quite the awful language when it comes to really understand each other. Wonderful for quick, brief written communication, awful for everything else.
@@MrJerichoPumpkin It is an expansive enough language for precise and clear communication but it requires having a very broad vocabulary that most lack and using the more precise words can be cumbersome.
If I work @ a used book store and you bring me a book asking how much it costs and I tell you $1 and then a tree falls in the woods with no one around, did the water actually flow uphill?
The main problem is that no one talks like this, and it can be interpreted the spoken language way, the grammatically correct way, or the mathematic nerd way. Additionally none of these situations are realistic. These vague type questions are what make most test takers annoyed with academia's out of touch test makers.
@@SomePeopleCallMeWulfman no, obviously for nutritional needs, watermelons are distributed according to a person's height measured in Standard Melon. Everyone knows that. In standard day weather conditions, watermelons are rated at 1.412SM. If Matt is twice as tall as Sally and one watermelon shorter than Walter who is half again as tall as Luisa who stands 4.5 watermelons tall, how many watermelons does Sally get? It's just simple math.
I think it's just a confusingly phrased word problem. I was thinking of it like sales tax or a tip rate, which is a kind of math people do every day. This book costs $1 (base rate, printed on the back cover) plus half its cost (50% sales tax because this is some sort of dystopia). Therefore the total price paid is $1.50. Makes sense, right? I think that's how most people approach this question, and who can blame them? I also see and totally agree with the $2 interpretation from a purely algebraic standpoint. But part of my mind just keeps asking "but why would you, an English speaker, ever ask this question this way?"
Simple. Because it's a "gotcha" moment. The people who want the answer to be $2 will make it 2 because they want to assume C= 1 + 1/2P where C=P even though there's 0 logic in the question that Cost and Price have anything to do with each other.
As an adult, you tend to factor sales price into things. But students learn from the ground up, and probably haven't made that assumption. It's a classic adults overthinking something a child wouldn't. If there was a question about it on the test, the teacher would be asked to clarify.
I think most of the world have taxes included in the price contrary to the USA which adds them after. Meaning only US citizens will think about something like that.
@@tesladrew2608it also doesn't help that the question is clearly trying to give a relatively complex problem in as few words as possible specifically to make it more ambiguous.
I'm used to these awkwardly written math questions. The reason why an individual would think that the answer is $1.50 is because of how the question is written. I would assume most people would read the question in two parts, Part 1: A book cost $1 Part 2: plus half its cost $1.00 + $0.50 = $1.50 Perhaps the question could be understood better if it was written like this, The cost of a book is equal to this: $1.00 plus half of the book's cost. Part 1: The cost of a book is equal to this: Part 2: $1.00 plus half the book's cost b = 1 + b/2 b/2 = 1 2*(b/2) = 2(1) b = 2 Alternatively, you can read the problem like this: The cost of a book is equal to half the book's cost plus $1. b = b/2 + 1 Same equation, you will still get the same answer of 2. If you are still having trouble understanding, then approach the problem slow, step by step, interpreting it mathematically. A book cost $1 plus half its cost. "A book" So we put down a variable. Let's say b for book. b The next word after "A book" is "cost" We can interpret "cost" as "equals to" b equals to The next word after "cost" is "$1" So now we have: b equals to 1 But we are not done yet. There is still more to be added to the cost of the book. The next word after "$1" is "plus" b equals to 1 plus The next words after "plus" is "half its cost" Half its cost means half of b, we can write half of b mathematically by dividing b by 2. So b/2 So we get: b equals to 1 plus b/2 b = 1 + b/2 The answer is 2. There is only 1 possible answer.
thats exactly what i did, i was a bit confused at first as to what the half is considered to be but then i wrote a simple algebra 1 equation and i used the same variables as you lol. only difference i wrote .5b instead of 1/2b
But that equation is flawed: It conflates different variables together. B = 1 + b/2 is false, outside 2. 10 = 1 + 5? 26 = 1 + 13? 1 = 1 + .5? For some reason, 2 is the only one I could find that actually works, lol. The cost is unknown. You can tell the two are seperate by the math, but also if you replace A Book with My Book: "My book costs $1 plus half its cost." (My book costs 5$). I don't tell you it's 5, but the cost is 5. Thus, the answer 2 is obviously wrong (in the interpretation that 1 is added to the cost).
@@xum0007 You are not stupid. I am waiting for someone to show me I'm wrong, lol, but I don't think so. It's talking about two different costs. The cost of the book, and then the final cost.
Imagine the question as the following interaction at a book store where tax is charged separately: You look at a book with a price tag of $1 (+taxes) You take the book to the cashier and asks, how much is the tax? He says, 50% (or half) the book price (tag) How much will you pay at the end for the book, plus tax? $1.50 In this interpretation it's perfectly valid to separate the question as: 1)the book costs $1 (shelf price) 2)plus half its price (50% tax over the original $1) 3) How much does it cost at the end (total = shelf price + tax)? This is what almost 90% of people thought when they answered the poll.
@@Federico-mj3si agreed, everytime the answer appears too simple, its probably a trick question. My point was to show that it is possible to interpret the question in a real world scenario that corresponds to the first instinctive answer people gave.
I also think even if we assumed Cost=price The statement doesn't say A book costs the *same as* 1+half it's cost So we can't just do x=x/2+1 ryt There is no relationship given in the statement A book cost, 1+half it's cost So we assume the cost of the book is 'x' We know that the new cost of the book(after discount) Is 1+x/2 What relationship do we have between these two linear expressions , it's none . In my opinion the book can cost anything For example the book was initially four dollars and after discount it's 3 dollars and this will be true for all values of x . So we really need a clearer relationship between 'x' and (1+x/2)
When I was around 3rd or 4th grade, during a problem-solving lesson (I taught myself with books and was and still am an avid math competitor), the book presented a different problem but with a similar concept. It states, "A ball and glove together cost $10. If the glove costs $9 more than the ball, what is the cost of the ball?". The answer was $0.50 (check for yourself). The whole chapter centered around that problem and the use of algebra to manipulate expressions that seem easy in disguise, and I never forgot that. It's crazy how you must focus on even such simple problems like these.
It's not the problems themselves that are tricky, it's the language used by the problems that makes it so tricky. If the problem had been laid out as "C=1$+1/2c", it would have been much easier to solve. But because our language hardwires us to think that "Well, the problem says that the book must cost 1$ because it says so, and so we add 0.50$ and call it a day", we get it wrong.
@@hjk4583 I didn’t necessarily say that the problem was tricky, but I get your point. Wording is very important in mathematics, and thus is a great example of a problem that messes with your brain. The AMC (American Mathematics Competition) can kill you if you don’t read the wording correctly.
Ironically, solved by a guy who was also told "You'll kill your father and marry your mother." Then proceeds to kill a man old enough to be his father, solve the mentioned riddle, marry the recently deceased man's wife. A great reflection on academia as opposed to any real world sense.
@@alt-q1y yes and the answer is "human beings" cuz in the context of the riddle, morning means the begining of life(we all crawled on all 4 before as babies), 2 in the evening(the middle of life as adult humans walking on 2 legs), and 3 at night(signifying the near end of human life, an old person relying on a cane to walk(making 3 "legs")
Yeah? Well, welcome to the real world, buddy. Where not everything is standardized for your convenience. These problems exist to make you use your brain in different ways, which in turn enables you to think outside the box when encountering real-world issues. That is why math like this exists in school: to help prepare you for life. Problem is, fools like you will never understand that.
I understand how you did it. My problem is just the first part of the sentence makes it sound like the book actually costs $1. Maybe if it was written differently idk tbh lol
I feel like if this question was written in a book for grades 1-2 (my child's grade) it would be $1.50.... I see stuff like this all the time in his work books 😂
@@bprpmathbasicsyou weren't careful enough to remove an entire variable, PRICE. Price =/= cost. Cost = c Price = X C = 1+0.5x This is unsolvable and the correct multiple choice answer on the original post is "I don't know".
@@duckheadbob I think that distinction is important if this was an accounting question rather than a grade school algebra question. That said I don't know which it is.
You can solve this with common sense. How many halves make a whole? Two. If a book is a dollar plus half its cost, that means the dollar already took you halfway there. So just double it. $2
@sailinsax1 and most people will use them the same way because it still makes sense to do so in normal casual conversation like if you buy something for $5 and someone asks how much it costs you'd say "it costs $5" not "the total was $5 🤓 " arguing about how it's wrong is just annoying semantics the whole point of the question is to be worded in a way which will make people understand it wrong to trick them
My first thought seeing the problem was: "It costs $1. We also need to pay an additional fee (tax, shipping, etc) equal to half of the cost. How much is the total price?" because that would be similar to real experiences I have had. After a careful rereading, I realized they meant: "The cost is equal to $1 plus half of the cost. What is the cost?"
That's arguably a more correct way to look at it because it more closely matches how we use prices in the real world. If you invert it -- a book costs $1 minus half its price -- that's a half-off sale, and you'd be right to say it costs 50 cents with the sale. So it makes sense that when people see the same format but as a premium instead of a discount, they'd apply the same reasoning and conclude $1.5 is the final price. That's _not_ incorrect.
@@truthseeker7815 Have you never bought something that was actually more expensive than the listed price? Because I'm very much used to the "cost" and the total cost being different. This is very much how the real world works.
Very tricky indeed. The ;problem is plain language: "The book costs $1" is a declaration, followed by "half the cost" since we have DEFINED cost as $1, half that is 0.50 But if we change the binding to somewhat unnatural "The book costs [ $1 plus half its actual cost (which isn't $1)]" a different solution exists. Consequently, two CORRECT answers exist depending on your language bindings. CostOfBook = $1 + (CostOfBook/2) x=1+(x/2) x = 2/2 + x/2 // establish common denominator x = (2 + x) / 2 // combine denominator 2x = 2 + x // eliminate denominator x = 2 // subtract x from both sides
I disagree that the first interpretation is valid, for grammatical reasons. If you assume "a book costs $1" is a full clause, then it is invalid to stick on "plus half its price" to the end to get a sentence. This forces you into the second interpretation.
@@zmaj12321 "This forces you into the second interpretation." No, it does not. I go into a bookstore and see a sticker, $1, that is its published cost. But there's a sign at the register, plus half the cost. So it's $1.50 You can plainly see by these comments that nobody is FORCED into your particular interpretation. This question is a linguistic exercise and I suspect Google's A.I. is training on this and similar ambiguities so that I can learn (1) English is probably always ambiguous and (2) how to explore the various possible branches, all of which are "correct" but one of them was "meant". A much more common variant of this involves the division operation; some people assume that everything to the right of the divide symbol is part of the denominator; others (myself included) treat ONLY the very next term as the denominator in the absence of parenthesis.
@@thomasmaughan4798 The first interpretation is contradictory. Because you assume first that the book costs $1, but then it also costs $1 plus half of a dollar. That would be like schrodinger's book, having two different prices at the same time
@@thomasmaughan4798 My point is that the problem, as presented, is a single English sentence. So a valid interpretation should follow English grammar rules. If I'm reading you right, then you are taking the sentence "a book costs $1 plus half its cost" and treating "a book costs $1" as an independent clause, but the problem is that the rest of the words have no way to fit into the sentence. "Plus half its cost" doesn't have a verb in it, so it can't be its own clause. It only works as a modifier on "$1".
@@maximofernandez196 "That would be like schrodinger's book, having two different prices at the same time" Yes; it has rather more than two. My daughter was puzzled by the price of a dress: Price is Price minus 10 percent. What it *means* (probably) is "price you pay" is "price marked" minus 10 percent OF "price marked". It is common to not write all that. Consequently, "The book costs $1" is a simple declaration. People that process language as you go along will store that declaration in their mind. Then add half the cost; okay 50 cents. The price I pay is thus $1.50 People that read the entire sentence *before setting up the problem* MIGHT bind it differently: Cost of a book is X. X is $1 plus half of X. Solve for X. But that is not what is written. A shorthand might be "The cost of a book is [$1 plus half the cost] which requires some algebra to solve: X = 1 + (x/2) BUT AS WRITTEN it is perfectly legitimate to process it this way: Cost = 1 + (1/2) A computer would do it that way, too. Cost = 1; // "The book costs $1" Cost = Cost + (Cost/2); // "plus half the cost" Print Cost Obviously the variable "cost" will be modified and end up being 1.50
It's also grammatically ambiguous and ill defined logically, so... Math teachers trying to trick people with English always works out well. Cost != Cost in this sentence, which makes the whole thing a lie, not a trick. They could have said "Costs a customer $1" and it would have been enough for most to solve it.
Even though the OP made the "answer" $2, the real answer to the question they made is actually "unknown," because the way the question is worded it is not made clear if "cost" and "price" are the same or not. If they are the same, then $2 is the answer. But if "price" is just what the book is listed as and "cost" is the total amount the consumer pays (the sum of "price" and extra fees such as sales tax), then $1.50 is possible but not the only possible answer, as the total listed price is never made explicit.
I assume most people looked at it how you would most often see it in the real world... Like, if a sign in a shop said "Price: $10" and next to it says " -1/2 Price", you would know you're meant to assume that the current sale price is either $5 ($10 with half off) or $10 (that it's already half off of $20). You wouldn't say, "well, the sign said it was $10 - 1/2C, therefore it should be $6.67". Not exactly the same since it's written out, but, it's a fair interpretation in my opinion.
Semantics, the cost can be calculated at $2.00 using the equality shown or the cost can be %150 of the original price. Since the original price isn't given the problem can't be solved in context. However, since the available answer options don't include an option for the percentage calculation the logical conclusion would be that the person who formatted the question intended the tested to use the equality in the former shown, even though it is assuming that price and cost are being used concurrently.
A book costs $1 plus half its cost. Seems pretty straightforward to me. Just because the answer isn't immediately obvious and you have to think about it for a moment doesn't mean there's a problem with the wording.
@@bakersmileyface This is the explanation I see nobody else using. Multiple interpretations. The English language is not straightforward, and this problem was intentionally worded so people read "A book costs $1" before anything else. I would have answered 1.50 like everyone else, because it is the most logical interpretation of the problem for most native speakers. So many comments here are basically saying "you're just bad" if you don't read the problem as the poster supposedly intended. $1.50 is correct if you interpret the sentence as a book costing $1, then having half that cost added on. $2 is correct if you mentally imagine a parentheses surrounding "$1 plus half its cost" to separate it mentally from the former half of the problem. Without a visual like parentheses to separate the cost from the $1, though(like a proper rephrasing of the question to be less confusing), it would be correct to assume either solution. tldr; You're not wrong for interpreting the equation the "incorrect" way, nor the "correct" way. Cost = 1 TotalCost = Cost + 0.5Cost TotalCost = 1 + (0.5 * 1) TotalCost = 1.5 Edit: And for the record, if there's 84% of people in that poll getting the same "wrong" answer, despite it being such a simple algebraic problem, maybe, just MAYBE it should be considered flawed execution. Y'know, instead of pretending everyone's just stupid when they've been intentionally tricked to get clicks on social media.
@@nebulavaa Yup. Another possible interpretation is if you take things in the literal sense of the word, this problem can't be solved. 'Cost' and 'price' have different meanings in the English language, although they're often used interchangeably because their meanings frequently coincide. If this problem were to be interpreted by definition of the word then we couldn't find out the cost of the product because we don't know the price and we aren't given enough information to determine the price.
@@bakersmileyface Thats not actually true, since it says cost and cost. There is only one way to interpret this in English. The way the sentence is written, in English and Math the answer would be 2$
@R.P.-hw2rq If you are an engineer, and have a customer who is very bad at giving relavent info in a coherent manner, you're basically working with this kind of problem
@@R.P.-hw2rq You would think that, mostly because that makes sense, but some people take it as an insult if you ask for more info, or think you are stupid. Have legit seen the sentiment of: "You're the engineer after all, figure it out, it's what you're paid to do."
@@wlonsdale1that is fucking hilarious, because it takes like 2 seconds of conversing with genxers and boomers to figure out that this statement is stupid. Everyone has issues with logic puzzles, it isn't a generational problem.
I haven't watched the video but i would write it algebraically using x to represent the cost of the book: x = 1 + (x/2) Solving for x would give x = 2 Overall the question is worded poorly and seems like is was designed to be tricky.
If I go to a garage sale or yard sale and they have a box of books and a sign that says ( a book cost $1 + half it's cost ) I'm going to pay $1.50 Unless I make a deal like 10 books for $8
This kinda question was viral a few weeks ago in Indonesia. I think its more like a language trivia rather than a math trivia. [A book costs $1 \\ plus half of its price] or [A book costs \\ $1 plus half of its price] So I think it should've been solved by a linguist instead, uhm, I guess(?)
A note to test takers: understanding the logic of a word problem will save you a lot of missed points of an exam like the SAT. You can even eliminate some wrong answers without having to do any math
I don't remember anything even remotely like this on the SAT when I took it. The math was just math, no jumping through hoops trying to guess what a sentence meant, as playing word games on a math section is just insanity. This was 2006, though, when there was still a little bit of common sense in the world. .
@@rodafowa1279agreed with you there. We had very little word phrasing nonsense in mathematics in the late 90s/early 2000s in high school. Nowadays I see a lot of this and it makes me wonder what the point of it is?
@@xocomaox It has to be some type of planned sabotage to make the next generations dumber and dumber. There are people out there who legitimately don't know how many States are in the US, and they've lived here since they were born. I'm not talking about kids, BTW, I'm talking adults (allegedly, anyway).
It's all for that "gotcha" moment, so you can go "um, actually" on everyone and make yourself sound super smart. Or at the very least, call everyone else stupid. Because you can't be on the internet without using a single question to give you confirmation bias on how you view the world and the people around you.
"Oh boy. Time to get my chart out to determine which series converge under which conditions." I love how mathematicians just casually recall, "Ah yes, it's a geometric series which means it converge when n > ..." No. I gotta look that one up.
@@papopepo69because the price of the item you buy isn’t guaranteed to be tax-free and free shipping. Price + tax + shipping = cost. Just like the price tag you see on a car isn’t what it’ll cost you.
The problem with questions like this is that they are erroneous in their initial wording, which is what causes confusion. In this example it says that the book costs $1 plus half its cost. That’s instantly confusing and doesn’t explain the question correctly
This also happens in accounting as well, especiallh on countries with English as their 2nd language. It infiurates me how in my country, when I had assessment test they have very poor grasp of grammar and sentence structure.
Yeah, that part was bad. I had to return to the screenshot at the beginning… there were 2 words used, cost and price. The explanation became more confusing
Quite confusing at first. But to understand it better, you can rephrase it as: the difference between the full cost of the book and half of its cost is 1 dollar. That means half of the cost must be equal to 1 dollar as $1 plus half of the cost is equal to the full cost. Therefore the cost must be $2.
Omg. I got the right answer. Im 67 and was taught to do all math on paper. If you can explain it to u our children that it is unlikely they will ever have to figure out what time trains arrive, or how old bob and his father are, BUT, it teaches you to problem solve, which you WILL use all of your life. For example, your credit card charges you 23% interest on unpaid balance. You go to a store and see an item you kinda like, but its 15% off, so you get it on sale, and it lands in the back of your closet, where it stays unworn, but you say, it was on sale, no big deal. But it is, because you only paid the minimum payment on your credit card, so the shirt you purchased cost more than regular price over and over and over. Pay cash!!
Why don't they communicate that in the question? "The books price is 50% of its initial cost plus 1 dollar" for example. Its unnecessarily complicated and willingly sparks confusion.
Because your phrasing suggests that there were two prices, an original one and a later one that was half the original plus a dollar more. That phrasing makes the problem impossible to solve because your "initial cost" isn't given.
All my teachers, from middle school to my masters, used to say the same thing. Good use and understanding of language is of outmost important in mathematics, that's why you should never imply or make assumptions of your own, you should only say exactly what you mean and vice versa. Back when i was a student i used to scoff at that, but now that i myself teach math, i can understand exactly what they meant. This problem demonstrates exactly that.
There's a simpler way. The price has two parts: 1 + half of the total. Therefore 1 must also be half of the total (one half gives the total only when added to the other half), therefore it costs 2. To verify: book costs 5 + half of total. 10 = 5 + 1/2 * 10 = 5 + 5 = 10 For every C = n + 1/2C the solution is 2n. What about C = n + 1/3C + n Then C = 3n
If the book was $10 last week, and this week the price increased by half, then what is the current price of the book? If a book costs $10, and I sell it for half price plus a dollar, then how much money am I selling the book for?
@@juliavixen176 if last week it was $10 and the price increased by half of last week's price ($5) then it costs 10 + 1/2 * 10 = $15 now. This is different compared to the original problem as here you have 2 prices: old price and new price. If you're selling it at half price plus $1, you're selling it for 10/2 + 1 = $6. Here you also have 2 prices: actual price and how much you sell it for (which is below its actual price)
I know grade school student's homework with wording that is as confusing as this. Or at least its needlessly tricky, and I say that because there are a million ways to rewrite the problem that are way less stupefiying. Half of the things they get wrong is just because they don't expect to be tested on their reading comprehension in math class.
In the original post the first statement uses both the words “cost” and “price.” It then asks for the “cost” in the final question. No wonder so many people answered 1.50, because the word “cost” was already originally defined as $1. This is a word problem, not a math problem, right?
@@papopepo69 but isn’t this also incorrect? If price and cost are distinctly different then the formula should be: C = $1 + 0.5x where cost=C and price=x? So, as others are pointing out, it’s actually unsolvable. The way most people read English, it’s super easy to assume that cost = $1. That’s all!
@@K-PastorMatt Why would you assume the price is 1$? The full statement is: A book costs 1$ plus half of its price A book costs (1$ plus half of its price) A book costs > Price of the book Price of the book = 1$ + Price of the book/2 I dont understand your point of view, could you explain your train of thought?
@@papopepo69 I’m just bad at reading and math. I imagined the statement like this as I read it: (A book costs $1) plus half its (price). What is the books *new cost?* as if the question were asking for the original cost plus half its price. Thats people might assume it was $1
It's called an Equivocation Fallacy. Basically, the video maker had some bad logic and it resulted in $2 being the answer. The actual answer is $1.50. It's not an assumption that the book's initial price is $1. That is simply the correct way to read the sentence.
I will never have patience for math questions that can be interpreted in various ways. Like for instance if you take it to mean; C+1/2C=$1, C=1+1/2C, or Ci=1 C=Ci+1/2Ci. C can be equal to; 67¢, $2, or $1.50. And there is a valid argument for every answer. That argument is “Grices maxims of communication, specifically manner and quantity. That is to say the question can be written as “What is the price of a book if it’s cost is $1 plus half the price” this aids to the construction of the equation P=C such that {C=1+1/2P} where, since C=P, it can be rewritten as P=1+1/2P. Or better yet. A book costs the sum of $1 and half of the cost. But let’s be real folks, this question isn’t about simple algebra, it’s about the recognition of variables and correctly identifying how to work with them. This question is an extreme of vagueness. The real world is full of dumbasses that don’t know how to ask questions properly, that’s what the question aims to prepare you for. I for one, will be quitting any job where I have to deal with stuff like this on a regular basis, because it’s so draining to report to someone who is bad at communicating, when their sole job is proper communication.
That would certainly be a problem if any of the alternative interpretations were at all reasonable. You might as well complain that the question makes no sense if you assume that $1=$2. True, but irrelevant. There is no vagueness, only tragically poor reading comprehension.
This must be why language interpretation and math are separate entities. Both answers are accurate, as both ways of understanding the question are accurate. Nevertheless, i hold to my original thought process of this being unsolvable
I was thinking of going at it from an infinite series approach. That part of math class is kind of hazy to me but I'll try it out, it might not approach a limit though: 1+.50=1.5 1.5+.75=2.25 2.25+1.125=3.375 Ok it's divergent, lets go with your answer, unless it's infinity dollars
That approach is correct. You need to do the following though: 1 + 0.5 = 1.5 1.5 + 0.5/2 = 1.75 1.75 + 0.25/2 = 1.875 1.875 + .125/2 = 1.9375 And so on.... Or another way to think about it: Basically, you are adding half of the cost to 1, getting the new cost of 1.5 However, you already added half of 1, so now you only need to add half of 0.5 to it Then you add half of the new added part and so on. You can also write it in your format like this instead: 1 + 1/2 = 1.5 1 + 1.5/2 = 1.75 1 + 1.75/2 = 1.875 1 + 1.875/2 = 1.9375 In other words, you are adding half of the new price you get to the 1 every time, since you know that 1 + half the price is the actual price. The benefit of the first one is that we can easily write it as 1+ sum(1/2^n) with n going from 1->infinity, the infinite series being a geometric series that converges to 1, so 1+1 = 2 total.
I love your videos, I have a degree in math, and this problem makes me irrationally angry. I always fall for semantic tricks at least once before I figure it out. Anyway just wanted to say your videos are great refreshers on the basics I learned years ago to help keep me sharp! Keep up the good work!
It all comes down to what the person asking it means by the question. This is one of those things where, at my company, someone might literally call a 15minute meeting just to get the full context of the question understood before figuring out next steps
@@gnack420 there's a difference between confusion and colloquial ambiguity. The word "cost" is used twice, which may or may not take on more than one meaning, as well as the word "price," which may or may not be referring to the same thing as one of the uses of "cost" - all due to the varying colloquial ways in which different people use these words. Yes you can try to use context clues to narrow it down but ultimately, in real life contexts, it's best to exercise due diligence and ask the person what they mean. Otherwise, the very thing you assume is obvious turns out they meant something else.
it's stuff like this that give students trust issues, especially in math. In layman term it would be $1.50, but in a mathamatical terms it's $2.00. Bruh 💀
Finally a math problem that I was able to solve on my own, and fairly easily. It was obvious from the wording that it was not a tax-like situation where you just add the half onto the base price. It was half of the unknown total cost.
You’ll be alright. I sifted through the comments and found that an easier way to understand this is to word the sentence as follows: - A book costs… $1 + half it’s price, or - A book costs half the price + $1 Apparently, breaks can help a lot, be it for the mind or in sentence phrasing
@@theblinkingbrownie4654Yes, but using calc that has lim() shows that target price closes forever towards 2 dollars. So it's kind of clearer and one can do any kind of derivative/integral etc to show the "target" i.e. closest price-point forever is +2 dollars. Input 3 dollars and it goes above, input 2.2 dollars it's still bit above etc etc
This is why I sucked at math in highschool, I was bad at English but as soon as i started college they stop asking math questions like this and became questions like I learned in 4th grade where it was like 2+2= X.
The total cost is $1.50. You are just reading the sentence wrong. Proof: the book costs $1 plus 50% tax. Total cost of book is $1.50. You’re creating an expression that stems from misunderstanding the sentence. The expression should start as: C + 1/2C = X. Solve for X when C=1.
The answer is still present in the question. If the only disputed amount is “half the cost”, then we just infer that $1 makes up the other half. If the question read “the book costs $1 plus three quarters of its cost” we can automatically infer that $1 = one quarter of the book’s and solve from there.
The reason that the first equation (non algebraic) started with $1.00, and it was assumed that the book’s cost was $1.00, is that the sentence begins with “A book costs $1.00.”
Another way to read it is the cost is infinite because you're adding $1 to half the cost (however much that is), but since you've added the $1 the cost increased, making half the cost also increase. Half the cost increases infinitely 'pulled along' by the fixed value of the $1 addition.
Exactly. Then calculate using lim(x), x->C where C is cost of the book, you'll get to infinite close to 2 dollars. I don't care about how you put the math, but close towards C from up or down, use any formula (derivate/integral) what you like. Or try 3 dollars and see it's wrong, above target price and adjust bit by bit.
Yes, as he formulates it. The best criticisms of this I’ve seen has emphasized that “A book costs” isn’t an independent clause, and so setting C is an interpretation rather than the One Answer.
Just like most of these types of online math problems, the issue is the semantics. In normal everyday English you would never ask this type of question. We're used to answering the following question: "The book costs $1. Add half its cost to the final price. What is its final price?". With the correct answer being $1.5. That is the normal question. So, when we see a question similarly phrased we will assume its just the previous question but phrased in a quirky way or lazy way.
Exactly, it's an impractical question. How would anyone ever *know* the starting information -- that the item costs $1 plus half its cost -- unless they *already knew* it cost $2? And if they already knew that, why would they be asking the question? The question is useless, has no applicability; it exists only to pose a confusing puzzle.
@@goodmarowhat do you mean how would anyone know? The question literally tells you that the books costs "$1 plus half its cost". The thing with such questions are that they help you understand abstraction which is not tied to any language. That is the core part of the question - to "confuse", because you are trying to solve it with some semantics of English language, while it has one clear logical solution. And the solution will still stay the same, no matter what language you are speaking
@@holeintuniBut why would anyone ask such a question? To formulate that "$1 + half its cost", the person saying so would have to know it cost $2 -- and then why wouldn't the person just come out and state it simply like that? Especially if they want repeat business?
The original question has 2 separate items "Cost" and "Price" => from the original text shown "A book Costs $1 + half its Price" This means the Cost (what the book store pays)= $1 + 1/2 Price (amount the store charges customers) Cost = $1 + (Price/2) Cost-$1 = Price/2 2(Cost-1) = Price another what to say that is the Mark-up is $1 less than 100%
At first I thought this entire way of going about it was ridiculous… I was wrong, you made it make way more sense than any teacher or professor has. You’re a legend my man
Every time he says “we don’t know how much it cost” “we can’t assume the price” “let’s make it C because it could be anything” I just glance to the top left of the screen where it says A BOOK COSTS $1 in giant black lettering. I would argue that all that math, while technically correct, is practically wrong. No one (obviously veeeeerrrrry few people) would interpret the question that way, and in linguistics, there are no rules but majority rules.
Using two different words, cost and price, implies they refer to different things. Giving them the same variable is probably wrong. C = 1 + C/2 is wrong. Should be C = 1 + P/2.The right answer is, I have no idea.
No, let's think about our actual experiences. When do you ever pay retail price after a discount? Price is what the tag says, cost is what the customer pays after discounts and fees. It's clearly stated by Redditor, COST= 1+PRICE/2. Two variables. No clear solution until PRICE revealed.
The simplest way is to just stress the incorrect conclusion: if you say the answer is 1.5, then try working backwards through the equation. Half of 1.5 is .75, not .50, so suddenly the answer changes to 1.75. When the answer is 2, however, the equation remains consistent.
...or just write better equations. A good worded equation means that there is only one way to interpret it. In this case, there are two. (A book costs $1) + half its price (half of 1$) A book costs ($1 plus half its price) Let's eat Susan vs Let's eat, Susan situation
@@verchiel_8295 There already is only one way to interpret the original wording, if thought carefully. I don’t feel either of your alternatives explain to people the logical pitfall which led them to the wrong answer.
We are never really told the total, just given a set of potential answers. I maintain that both $1.5 and $2 works. If it were in the list, $301 would do equally well. If we do 1 + x/2 then x could be 1, 2, or 600. I see no reason to accept $2 as the final answer. The question is a disaster.
@@maevixie7041 to answer for him. The premise is not x= 1+x/2. but y = 1+x/2. Because nothing say that the initial price (x) is equal to the final cost (y). you assumed it but it's not part of the enonciation. What he was saying is if the initial price is 600 then the final cost would be 1+ (600/2) = 301. you can challenge that with any possible initial price and get a different result for the final cost, making it impossible to get a singular answer.
anyone asking this question is looking for $1.50 as the answer. for example, you're given a list of books you can order, with a base cost for each book and a note that says the final cost will be the cost + 1/2 the cost (aka 50%). the answer they want for a book listed at $1 base cost is $1.50, NOT $2.00. there is no plausible reason to want it calculated the way our host has done.
“A book costs $1 plus half its cost”, *as a sentence in english,* would normally mean $1.50. To interpret it the way necessary to the “equation”, you’d have to read the sentence in a way that is unnatural for English speakers; the correct way to word it would be “A book costs half its price, plus a dollar.” Either way, of course, the sentence lacks the information TO determine the cost of the book, *unless* the answer is $1.50-the only reason you would say the answer is $2, is because the original question was NOT an equation at all, but multiple choice, and 2 was the only other *possible* answer *of the ones provided,* other than 1.50. Otherwise, literally any number greater than 1.01 would be equally valid. However, again, that doesn’t matter, because the question is worded incorrectly for actual English speech.
@@forbidden-cyrillic-handle This maths only works with the options given and the way he broke down the values, if the book has a known value and is say, worth $20 then the answer based on the way the question is worded is $11. (10 + $1)
@@elusivecamel Your first answer was mathematically correct(? assuming cost and price are different) but didn't make sense, your new answer is mathematically incorrect and doesn't make sense 💀
This is why people hate math, because it's trying to be more clever than it really is. When using the word "costs" following the only noun in the sentence "a book", it is not inaccurate to deduce that the book costs $1: "A book costs $1". If this were on advertising copy and the business sold the book for $2, people would be upset and (correctly) deduce the shopkeeper was being misleading / engaging in false advertising. The fact you have to break out a whiteboard and to factor this out is more than enough proof that this can't be done at a glance (for most people). If you want people to take math more seriously, stop engaging in semantics and start writing better questions.
Basically the added cost HAS to be half the cost because its literally the other half lol It could work with a quarter or a tenth etc... just need the correct proportioning, example: Book= 12$ 9$ + quarter of the cost (3$) = 12$ I made one you can try if you want: A book costs 89.36$ plus a fifth of it's cost? How much does it cost?
@@Ultimine1 Excellent example. It actually helped me really grasp your initial point. If something is x plus one-fifth of itself, clearly x has to be the other four-fifths. That's probably an even better way to think of it. Straight to the point and relies on the simplest thinking to get there.
Thanks, I saw a lot of confused people still in the comments so I tried to figure out a simple explanation to help people understand easier. Glad you liked it!@@cajonesalt0191
This assumes that "cost" is equal to X and that "price" is also equal to X - which in english they are not exactly the same thing. In reality cost = X and price = Y
I didn't get this right because OP unnecessarily changed the terminology in the question. Cost and price mean the same thing logically but linguistically they feel like they're indicating separate values. I set the variables COST=C & PRICE=P so: C=1+1/2P changing price to cost in the questions wording does clarify and I think defeats the intended purpose of the question. :/
It's 1.99999999999999999999999999999999999 (infinitesimally close to 2), but since we only deal with centesimals for money, it could be truncated to 1.99 or simply rounded up to 2.
The problem is written in such a way as to make you think it is saying "the book costs $1.00" instead of the saying "the cost of a book is equal to $1.00 plus half of the books cost. The problem is written poorly.
@@t_c5266 yes fair enough I should have clarified that I meant that no actual number of iterations will get you all the way there, if you were to try and manually work it out this way. But yes as an infinite series it is = 2
Yeah, that should be enough to say that the first interpretation doesn't make much sense. You can also say that the book cannot cost $1 and $1.50 at the same time.
Before watching I think I figured it out. I just set up an equation. Let the total cost of the book equal x. From here use x=1+1/2x. (Subtract (1/2)x from both sides). (1/2)x=1 (Multiply both sides by the reciprocal of 1/2). x=2.
