SOLUTION: 2/5 of A's money is equal to 2/3 of B's money, and $48 is the sum of their money. Determine A and B's amount. 2/5 of A's = 2/3 of B's. 1/5 of A's = 1/2 as much as 2/5, and 1

Question 1204785: 2/5 of A's money is equal to 2/3 of B's money, and $48 is the sum of their money. Determine A and B's amount.
2/5 of A's = 2/3 of B's.
1/5 of A's = 1/2 as much as 2/5, and 1/2 of 2/3 = 1/3 of B's.
Not sure how to proceed.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Two quantities of money: A and B.
From given, you can understand that .

The first sentence literally means .

You will have no trouble solving the system.

So the system can be changed to

Try this:

and ADD...

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

Given the fact that 2/5 of A's money is 2/3 of B's money, you had the thought of, in effect, dividing each fraction by 2 to see that 1/5 of A's money is 1/3 of B's money.

That was potentially a good thought; but it didn't lead anywhere that you were able to see.

In fact, one good start on the problem is to MULTIPLY both fractions by some number to make the information easier to work with. Since the denominators of the fractions are 5 and 3, we can clear fractions if we multiply both of the given fractions by 5*3=15:

--> --> -->

Then, using A+B=48, there are several possible paths to the solution.

A couple of basic algebraic paths are these:
(1) Change A+B=48 to B=48-A and substitute "48-A" for "B" in 3A-5B=0
(2) Use elimination with the two equations A+B=48 and 3A-5B=0

I myself prefer a less obvious path to the solution, like this:

Given 3A = 5B, let A = 5x and B = 3x.

Then A+B=48 becomes
5x+3x=48
8x=48
x=6

and so

ANSWERS: A = 5x = 30; B = 3x = 18

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