The cost of your favorite coffee doubled, with 7% tax you now pay $12.50, what’s the original price? 

I just work the problem backwards ... 12.5 / 1.07 then divide by 2 = 5.841121 or (5.84)

OK, I got the answer you were looking for w/o difficulty, but your problem statement is subject to more than one interpretation . You don't say if the the 'original price' included taxes. I agree with others who pointed this out. It reminds me of a univiersity physics final exam I took 59 years ago where the hot shot young professor had us determine the maximum vehicle bank speed around a curve. I couldn't solve the problem b/c I needed the width measurement between the right and left wheels of the vehicle, and labeled that an unknown. Try as I could, i couldn't derive this measurement, and was thus stumped. I got zero for the answer and the professor told us that the problem gave that measurement as the "wheelbase" of the vehicle. I told him and showed him that I had correctly analyzed and solved the problem but thought that "wheelbase" referred to the distance between front and rear axles. He disagreed, and refused to even give me partial credit. He was a self declared sports car buff so I figured he must know better than me what "wheelbase' meant. He should have given me at least some credit, but no deal. I was too young to realize i should have gone over his head. Several years late i discovered that my understanding of wheelbase, not his,was correct. I'm still PO'd about it. Moral of story: yes students read the question three times, but teachers, also read your problems three times to be sure you are absoultely clear in stating a problem. Clearly understanding the problem is the very first step in solving any problem.

I make the original price to be $5.84

A simple enough calculation that I would have had no trouble doing, but I had to watch the video because the question did not make it clear if the sales tax or VAT as we would call it in my country should be included in the final solution. In the UK VAT is included in the price of all goods sold retail excepting food and a very few other items considered essentials, like children's clothes, personal protective equipment like hard hats, overalls and safety shoes. food has VAT if there is a service included (I.e. if you bought it from a café or a vending machine that would be a service as apposed to buying the ingredients and making it yourself.) So here we would expect if the new price was double the original price you would half the new price to answer the question and treat the tax as a red herring. Don't you do that in America? or is it the net of tax price what you would see on the price list? I guessed that was what you intended, however were I a student taking an exam, i might spend more time worrying about what the question meant.

2X + 7/100 x 2X = 1250 (cents and new price). Result: 2,14X = 1250 => X = 1250/2,14 = (using my calculator) 584 ct. or $ 5,84 (original price).

Once again, an ambiguous question and a turgid rambling answer.

If you're smart enough to solve this problem, you're also smart enough to not buy a cup of coffee so expensive. Ergo, the problem is hypothetical. So tge next hypothetical question is: Who is dumb enough to pay over 6 bucks for 1 cup of coffee?

In determining where to round up your answer or certain figures before you get your answer (In this case, the decision is between 5.84 and 5.85.), that depends on what the governing body that collects that sales tax does when it has to round up something to get the final price. So, if going past halfway means rounding up, then the answer has to be 5.84 since 12.497 rounds up to 12.50 and since 5.85 would result in 12.52 being the new price plus 7%. If you always had to round down then the answer would have been no solution since 5.84 would have led to 12.49 while 5.85 would have led to 12.51.

surely sales tax appplied to the original price....

1.07 × 2 × price = $12.5 Solve. Easy problem.

I understand your algebra but it was the wording that threw me off course

I think every answer given so far is incorrect. In fact, John the Internet Math Man gets it wrong, too. Look at the damned question: "Can You Solve?" The correct answer is YES. Any attempt to determine the math - the original price was $5.84 - is misguided.

got it 5.84 logic immediately brought me to 5.90 then 5.85 however, your formuala was great. it was faster for me to 'brute force' it than to try to create your formula. thanks for the fun

How much was the original tax. Surely they taxed it something originally.

Assuming the tax is unchanged, you were paying 6.25. If that was for an 8 oz cup, you were paying $100.00 per gallon for coffee. Stop complaining about the price of gas.

Solved at the thumbnail, I'm getting an original price of $5.84. The new price including 7% tax is $12.50, or 1.07 * pre-tax price. $12.50 / 1.07 = $11.68 = new pre-tax price. Since the new price is double the original price, $11.68 / 2 = $5.84 = original pre-tax price. (Adding in 7% tax makes the original taxed price $6.25, half the new taxed price, but I don't think that's the answer to the question asked.)

Yet again, we have extraordinarily sloppy construction of a mathematics word problem. You really should be able to do better than this. I calculated the answer you want in seconds, but it's not the answer to the question you actually asked. The punctuation in the question is terrible. I presume that is meant to be a full stop (period, for you Americans) after "doubled", because a comma makes no sense. With that out of the way, the question doesn't say anything to suggest that the tax rate has changed, so the obvious answer is that the original price was half of $12.50, i.e. $6.25. However, from watching the video, it's plain that you had in mind that the tax rate was 0% not 7% before the price rise. Or alternatively, you aren't imagining a change in the tax rate, but when you say "original price" you don't mean "original price", you mean the portion of the original price that isn't tax. It is beyond belief that you expect your students to read your mind like that. Put. ALL. The. Information. In. The. Question!!! If you don't put all the information in the question, then you have no choice but to accept multiple different answers as correct.

Hi John, You're a great Mathematics Teacher, and a good man. My wife and I are learning, practicing, and relearning math through you. Thank you Sir.

My favorite coffee is . 99 ¢ at McDonald's, and that's good enough for me.

These questions' difficulty is converting the WORDS to an EQUATION. Thus the term "word problems." Step 1: Assign a symbol for each parameter O : original coffee price C : checkout price = $12.50 T : tax = 7% Step 2: write equation(s) C = (1+T)(2×O) $12.50 = (1+7%)(2×O) $12.50 = (1.07)(2×O) ($12.50)/(1.07)(2) = O $12.50/2.14 = O $5.84 = O ans.1 Verify 2 × $5.84 = $11.68 $11.68 × 0.07 = $0.82 $11.68 + $0.82 =? $12.50 $12.50=❤$12.50

(12.50/1.07)/2 = 5.84 (previous cost of coffee before added tax). 5.84/1.07 = 6.25 dollars assuming the tax was in existence when the price was lower. Cost of coffee now before tax $11.68 Tax on coffee now $00.82 => coffee + tax $12.50 Previous Coffee cost no tax $05.84 Previous tax on coffee $00.41 => coffee + tax was $6.25

The answer depends on if tax is added before or after the doubling.

($12.5/1.07)/2=$5.84

I'm now paying $12.50 with the tax included. Before I was paying $12.50 / 2 without the tax. I'm now PAYING twice as much so I was paying $12.50 / 2 = $6.25. The PRICE of the coffee didn't double. The COST for me to buy the coffee doubled with the 7% tax.

to include sales tax you would multiply the amount by 1.07. So to remove the sales tax you simply divide the amount by 1.07. Then you're left with the new higher cost of the coffee, the coffee doubled. So you then divide this amount by 2. ( 12.5 / 1.07 ) / 2 = 5.84 (approx)

12.50 / 2 / 1.07 = $ 5.84 with calculator. Could I do without if I really tried?

I got $5.85, I guess I rounded the wrong place.😊

Mathematics goes also with the same ethos: Practice makes perfect

You need to work on your sound. Your teaching is fine though.

surely the answer is $6.25 with 7% tax.

Isn't it quicker to divide 12.50 by 1.07 then divide that answer by 2?

I can't solve this nonsensical problem, I am NOT that idiot who'd be paying 12.50 USD for "a coffee" 🤪

Hmm I did it all in my head and got 5.68...

Original price = $5.84

As stated before just divide the 12.50 by 1.07 and then divide that answer by 2 and get 5.84 rounded

I don’t drink coffee

I did 12.5/1.07 to get the new price, then divided that by two to get the old price of $5.84.

agreed with my fellow solvers, $5.84 original price with tax

I say the original price is 15 cents but they just say the 12.50 price is inflation.

Time to start drinking a cheaper brand of coffee.

(12.50/1.07) /2

P = Orig Price S= Subtotal T= TAX, F = Final Price F = S + T S = 2 x P T = S x 7/100 T = 2 x P x 7/100 T = 14P/100 F = 2P + 14P/100 100F = 200P + 14P 100F = 214P 100/214F = P F= 12.50 P = 1250/214 HCF 2 P = 625/107 p = ~ $5.84

$5.82

$5.84

5.81

5.84

Let X = Current price of coffee before tax. Let Y = Original price of coffee before tax and doubling. Therefore…. X = $12.50 / 1.07 = $11.6822429906542 Y = X / 2 = $5.8411214953271

Thank you

I'm sure the tax went from 5% to 7% also so you have to factor that in.

The problem is properly worded. Nothing wrong with it.

get rid of joe biden and the dems,problem solved.

Even though it's nonsensical I'll solve it anyway: 12.50 = (op + 0.07 * op)*2 6.25 = op(1 + 0.07) op = 6.25 / 1.07 op = 5.8411214953 USD