Question 1204785
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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.<br>
That was potentially a good thought; but it didn't lead anywhere that you were able to see.<br>
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:<br>
{{{(2/5)A=(2/3)B}}} --> {{{6A=10B}}} --> {{{3A=5B}}} --> {{{3A-5B=0}}}<br>
Then, using A+B=48, there are several possible paths to the solution.<br>
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<br>
I myself prefer a less obvious path to the solution, like this:<br>
Given 3A = 5B, let A = 5x and B = 3x.<br>
Then A+B=48 becomes
5x+3x=48
8x=48
x=6<br>
and so<br>
ANSWERS: A = 5x = 30; B = 3x = 18<br>