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Prep ratio

by hakyology » Mon Aug 04, 2008 11:54 am
Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?




The answer is 1/5.

I got 1/4.

Please explain. Thanks in advance.
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I got 1/5

by Gaurav Tyagi » Mon Aug 04, 2008 12:48 pm
Let X= Alice's pay / month
let Y = fraction of pay (like 1/4 or 1/5 etc)
So, savings per month = XY
Savings for 12 monhts = 12 XY

fraction she is not saving per month = (1-Y)
Amount not saving per month = (1-Y)X

so,

3(1-Y)X = 12XY
3X - 3XY = 12XY
3X=15XY

Hence, Y = 1/5
Thanks,

GT
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by sibbineni » Mon Aug 04, 2008 7:54 pm
let alice take home pay be X for each month
let Y be the amount saved each month

then the amount that she does not saves=X-Y

then for 12 months she saves =12Y

The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did no12Y

12Y=3(X-Y)
4Y=X-Y
5Y=X
Y=1/5X

1/5 of the take home pay alice saves

I hope it is clear
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