Expert: Sherman D. - 10/16/2008

Question
The ratio of Meg's money to Anne's money was 3:5. After Meg spent $12 and Anne spent some of her money, the ratio became 2:7. How much money did Anne spend?

Answer
(x/y) = (3/5)
5x = 3y
y = (5/3)x

(x - 12)/(y - z)
(x - 12)/((5/3)x - z) = (2/7)
7(x - 12) = 2((5/3)x - z)
7x - 84 = (10/3)x - 2z
21x - 252 = 10x - 6z
11x = -6z + 252
x = (-6/11)(z - 42)

We know its got to be above 12.

For it to work out with whole numbers, x would have to be divisible by 6

So using the next number when you add 6 to 12, which is 18

18 = (-6/11)(z - 42)
-33 = z - 42
z = 9

y = (5/3)(18) = 30

So Meg had $18 and Anne had $30 to begin with.

ANS : Anne spent $9

if your wondering, if you were to use 24 for x, and then you worked it out, you would get -2, which you can't have.