SOLUTION: Andy, Ben and Cain had a total of $440. After spending, Andy and Ben saved 2/3 of their money. Cain spent 3/4 of his money and saved the rest. Given that they spent the same amou

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Andy, Ben and Cain had a total of $440. After spending, Andy and Ben saved 2/3 of their money. Cain spent 3/4 of his money and saved the rest. Given that they spent the same amou      Log On


   



Question 1184354: Andy, Ben and Cain had a total of $440. After spending, Andy and Ben
saved 2/3 of their money. Cain spent 3/4 of his money and saved the rest.
Given that they spent the same amount of money, find the total amount
they have saved.

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The three boys each spent the same amount; and Andy and Ben each saved 2/3 of their money and saved 1/3. So Andy and Ben started with the same amounts.

Let x = amount Andy and Ben each started with
Let y = amount Cain started with

The total they started with was $440:
x%2Bx%2By=440
2x%2By=440 [1]

Andy and Ben each spent 1/3 of their money, and Cain spent 3/4 of his; and Andy and Ben each spent the same amount as Cain:
%281%2F3%29x=%283%2F4%29y
4x=9y
4x-9y=0 [2]

Solve [1] and [2] by elimination

4x%2B2y=880 (multiply [1] by 2)
4x-9y=0
11y=880
y=80

4x=9y=720
x=180

Andy and Ben each started with $180 and spent $60, saving $120 each.
Cain started with $80 and spent $60, saving $20.

Together they started with $180+$180+$80=$440.

Together they spent $60+$60+$60=$180.

Together they saved $120+$120+$20=$260.

ANSWER: They saved $260.