40% taken first, therefore 60% remaining. 1/2 of 60% taken next, that is 30%.Therefore, 30% left. Then you ask 6 is 30% of what number? 6=30/100 * x. Then solve for x.
Yesterday I tried this one but I was all confused. I said to myself that I would sleep on it. And what do you know? Eurêka! I found the solution today. 200%. I'll take that Mr YT Math. ;) That being said and before watching I have to give the method I used. Since there was 6 books left at the end and Ann picked half of them that out of 3/5 left I came up with 3/5 times x = 12, x being the total of books. Then it was a piece of cake using basic algebra. x = 20. And yes teacher, I verified at the end this time: 2/5 = 8; half of 3/5 = 6, and 6 = 6. That was a good one!
If you mean Tim grabbed 'the' six books that remained, this is answerable. With 40% gone and then half of 60% too, those six would equate to 30% at therefore 5% per book. The initial 70% is thus fourteen books for a total of twenty.
Let x represent the number of books. (3/5)x books remain after Dan picked up (2/5)x of them. (1/2)(3/5)x books remain after Ann picked up (1/2)(3/5)x of them. Thus, (3/10)x=6 or x=(10/3)6=20 books.
With the cold weather this weekend, looking at the thermometer the following interesting thoughts occurred: 1. When is the C and F temperature equal? 2. When is the -C and F temperature equal?
this is a dandy question. let's try to write equations... Start by identifying variables: N.1 : total books on shelf N.2 : number after first removal N.3 : number after second removal N.3 = 6 N.2 = ? Ann picked up half yielding 6 N.2 × (1/2) = 6 N.2 = 12 N.1 = ? N.2 = N.1(3/5) Dan took 2/5th leaving 3/5ths N.1= (5/3)N.2 since N.2 = 12 N.1 = 12 × (5/3) N.1 = 20 VERIFY DAN took 2/5ths of 20 = 8 leaving 12 on shelf ANN took (1/2) leaving (1/2) (1/2) × 12 = 6
That is a lot of calculations... I would say Ann had a choice of 12 books and Dan could take 3/5 x 12 = 60/3 = 20 books. I am more concerned about the deflection of the shelf: f = 5/384 q.l^4 / EI
If Ann picked up 1/2 of the 'remaining books' and Tim picked up 6 books (i.e. the other half of the 'remaining books'), then there were 12 'remaining books' because 6 * 2 = 12. The equation that we need to use is then: b - 2/5b = 12 b(1 - .4) = 12 b = 12 / (1-.4) b = 12 / .6 b = 20 (There were 20 "books in total") Answer Check: Dan = 2/5b = 2/5 * 20 = 2 * 4 = 8 Ann = 1/2(remaining books) = 1/2 * (20 - 8) = 12/2 = 6 Tim = 6 Total books = 8 + 6 + 6 20 = 8 + 6 + 6 20 = 20 (so the answer is true) The simplified version is that Dan picked up 40% (2/5=40%) of the books (8) & the remaining 60% (3/5=60%) of the books (12) were evenly picked up by Ann (6) & Tim (6), hence: 6*2=12. 12/60% = 12/.6 = 20 books.
Just after the explanation of the problem ('d misread it at first), my answer is there were 20 books in total. Dan took 2/5 of the total. Together Ann and Tim took the other 3/5 of the books. Since Ann took 1/2 of the remainder, Tim took the other 6 as his half. so the remaining books after Dan is 12. Dividing by that numerator (3), 1/5 is 4 books, 5/5 is 20, and Dan took the first 8 books.
If Ann took 'half of what was left' .. leaving 6 books for Tim .. she must have taken 6 books. Which means that 12 books was the remaining 3/5 that were there after Dan took 2/5 .. and if 12 is 3/5 that means that there were 20 books to start with.
I did by saying, Ann took half the books therefore Tim and Dan took the other half If Dan took 2/5 of the remaining half then Tim took 3/5 Therefore 3/5 = 6 So 1/5 => 6/3 = 2 Dan took 4, Tim took 6 => 4+6 => 10 = 1/2 of the books 20 = all the books
2/5 = 40% of the total books, which Dan has already picked up. Therefore, the balance books available would be 60%, out of which 1/2 = 30% was picked up by Ann. Then, the balance remaining on the shelf is 6 books, which is equivalent to 30% of the total books isn't it? If 30% is equivalent to 6, 100% = 20, which I believe is the correct answer 😂
This is how I got there. for those who are wondering the 12÷3 comes from the fact that there are 3/5 of the books remaining, so find how many books are in 1/5 of the total you divide 12 by 3 to get four which is 1/5 of the original 10 times that by five to get 20
In the first part, you show what is left after Dan's take as (1 - 2/5)n. Shouldn't you show what is left after Ann's take as (1 - 1/2)(1 - 2/5)n? Or maybe (1/2)(3/5)n. It seems it would be clearer to keep the taken and the remaining in the same form. When i first ran through this problem in my head, i used the 2/5 that Dan took instead of the 3/5 that remained and came up with the wrong answer. When i checked it, i quickly saw my mistake.
There is a bit of a hint in the question. Since Ann took half of the remaining book, the number remaining is equal to the number she took which is the number Tim took.
This not maths but logic and does not need complex algebraic representations. Ann and Tim took half each of the remaining (three fifiths after Dan has removed two fifths) books, ie 12 books. If 12 books = three fifths then one fifth = 4 books and five fifths must = 20 books. By the way, the final sentence, as this is a maths/language question, should be in the past tense. As phrased, in the present tense, then the answer is Zero as Ann, Dan and Tim have taken them all.
