SOLUTION: if 1/2 of A's cookies is equal to 2/3 of B's cookies what fraction of the total cookies is A's cookies? how can we solve this.

Question 1144189: if 1/2 of A's cookies is equal to 2/3 of B's cookies what fraction of the total cookies is A's cookies? how can we solve this.
Found 4 solutions by Theo, MathTherapy, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let a = number of cookies A has.
let b = number of cookies B has.
1/2 * a = 2/3 * b
solve for a to get a = 4/3 * b
A has 4/3 * the number of cookies that B has.
solve for b to get b = 3/4 * a.
B has 3/4 8 the number of cookies that A has.

if you let B have 12 cookies, then A has 4/3 * 12 = 16 cookies.

16 = 4/3 * 12.
half of 16 = 8
2/3 * 12 = 8
half of the number of cookies that A has is equal 2/3 of the number of cookies that B has.

since you did not state how many cookies A or B had, the only thing you can do is to solve for the ratio of the number of cookies that A has to the number of cookies that B has.

alternatively, you can solve for the ratio of the number of cookies that B has to the number of cookies that A has.

A has 4/3 times the number of cookies that B has and B has 3/4 times the number of cookies that A has.

16 / 12 = 4/3
12 / 16 = 3/4

the only other consideration is that you would probably want the number of cookies to be whole numbers, although that is desirable, but not essential, unless the problem states that the number of cookies has to be a whole number for both A and B.

that's why i chose 12 cookies for B.
it made the answer come out to be a whole number for A and B.

Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!
if 1/2 of A's cookies is equal to 2/3 of B's cookies what fraction of the total cookies is A's cookies? how can we solve this.

Let number of cookies A and B have, be A and B, respectively
Then we get:
Total cookies:
Fraction of A's cookies to TOTAL cookies:
Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.

Although the post by @Theo is long, it does not contain the whole solution to the problem
and does not contain even an answer to the problem, at all.

So, I do not understand exactly for which purpose it was written.

For the full solution presented in a good style see the post by the tutor @MathTherapy.

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

Given: [1]

Multiply by 2 to get A in terms of B: [2]

The fraction of the cookies that A has is

[3]

Substitute [2] into [3] and simplify:

That's mathematically sound; but it looks a bit ugly. Let's see if another path is easier to follow.

Given:

Multiply by the LCD to clear fractions:

Given that equation, let A = 4x and B=3x. Then the fraction of the cookies that A has is

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