Dan picked up 2/5 of the books on a shelf. Next, Ann got 1/2. Tim got the last 6. How many books?

Рет қаралды 26,153

Күн бұрын

Пікірлер: 59

@aryusure1943 10 ай бұрын

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!

@Tokinjester 10 ай бұрын

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

@thomasharding1838 2 ай бұрын

Ann took half of the REMAINING 3/5 of the books left after Dan took 2/5, NOT half of the total. But in this problem, that still works out to 20 total.

@thomasraywood679 10 ай бұрын

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.

@skipbrewer8101 10 ай бұрын

total =20 head calculation

@ryanwalter5824 10 ай бұрын

Good for you do you want a cookie

@Dalgor_ 10 ай бұрын

For me it was much more simple just to do this in my head: let x = total amount of books x * 0.6 * 0.5 - 6 = 0 0.6x * 0.5 = 6 0.3x = 6 0.1x = 2 x = 20

@bogusfranz1503 10 ай бұрын

2/5 X + 1/2 (X - 2/5 X) +6 = X Simplifies to 4X + 5X - 2X + 60 = 10X -3X = -60 X = 20 😊

@thomasharding1838 2 ай бұрын

ASSUMING that the 6 Tim picked up were ALL of the remaining books left on the shelf (that was NOT a given fact!!!) There were 20 books in total. Dan had 2/5 (4/10) leaving 6/10 and Ann got half of that, 3/10, leaving 3/10. If Tim's 6 books was that 3/10, then 1/10 would be 2 books and 10/10 would be 20. Another Thumbs UP!

@wes9627 10 ай бұрын

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.

@merc340sr 10 ай бұрын

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.

@danielmadden9691 10 ай бұрын

2/5+1/2=9/10 leaves 6books which equals 1/10 implies=60

@ggb1377 10 ай бұрын

As an elementary math teacher this can be done using a strip diagram. Always helpful to draw a picture.

@Ayelmar 10 ай бұрын

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.

@tomtke7351 10 ай бұрын

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

@panlomito 10 ай бұрын

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

@ab_ab_c 10 ай бұрын

@@panlomito 12 / (3/5) = 20. Following your method, you should have written it as 5/3 * 12 = 60/3 = 20.

@panlomito 10 ай бұрын

@@ab_ab_c You're right, not 3/5 but 5/3. Thanks !

@buddyroeginocchio9105 10 ай бұрын

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?

@deercatchersoutdoors330 10 ай бұрын

Thanks for your content John, your test prep got me through my GED math. Much appreciated

@MrMousley 10 ай бұрын

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.

@bakerbill4274 10 ай бұрын

Did it this way in my head in about 20 seconds. The instructions should have said "using algebra to solve".

@terry_willis 10 ай бұрын

Elegant solution by Mr. Math Man.

@timdiggle5090 10 ай бұрын

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.

@mederickblack2369 10 ай бұрын

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.

@saleemsunthus3367 10 ай бұрын

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 😂

@pattyoconnell1950s 10 ай бұрын

12=3/5 4 =1/5 X=5/5 20 books

@Kleermaker1000 3 ай бұрын

This is a matter of calculation, not of algebra ( and easy too :) ).

@ab_ab_c 10 ай бұрын

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.

@motorbuzz4748 10 ай бұрын

20 in my head.

@paraglide01 10 ай бұрын

20. 6*2=12 /3=4*5=20

@fanofsteel9320 10 ай бұрын

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

@Jim-qc6gu 10 ай бұрын

Dan should have just taken the FIFTH of Jack

@charlesdempewolf6861 10 ай бұрын

Umm - I'm gonna go with zero books. Dan, Ann and Tim appeared to have picked them all up. (Rule of three...)

@raya.pawley3563 10 ай бұрын

Thank you

@aryusure1943 10 ай бұрын

Don't blame me for using algebra please. ;) I need the practice!

@StephenRayWesley 10 ай бұрын

2/5-1/2=1/3 ×6=18 /3 =6

@lpslpslpslpslpslps 10 ай бұрын

18 minutes to solve a problem that takes 10 seconds to solve

@KhmerUSA999 10 ай бұрын

The problem is Dan took first. if Dan just took 10 books and will be easy. 10+5+5 = 20

@ab_ab_c 10 ай бұрын

It would make it easier, but 10 is not 2/5ths of 20, so it would be wrong.

@richardl6751 10 ай бұрын

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.