SOLUTION: A woman spent two-thirds of her money. She lost two-thirds of the remainder and then had $8 left. With how much money did she start?

Question 661831: A woman spent two-thirds of her money. She lost two-thirds of the remainder and then had $8 left. With how much money did she start?
Answer by ReadingBoosters(3246) (Show Source): You can put this solution on YOUR website!
x = starting money
x - 2/3x - 2/3(x-2/3x) = 8
distribute the 2/3
x - 2/3x - 2/3x + 4/9x = 8
x + -2/3x + -2/3x + 4/9x = 8
in other words, dealing just with coefficients of x
1 + -2/3 + -2/3 + 4/9
with common denominators
9/9 + -6/9 + -6/9 + 4/9
9 - 12 + 4 = 1
1/9x = 8
Multiply both sides by 9
x = 72 = $72 started with
Proof
72 - 2/3(72) = 72 - 48 = 24
24 - 2/3(24) = 24 - 16 = 8
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