Alice's Take Home Pay

[okigbo]

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 $ that she had saved at the end of the year was 3 times the amount 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?

a. 1/2
b. 1/3
c. 1/4
d. 1/5
e. 1/6


Thanks.

[crackgmat007]

Is it D?

Let S be savings
I be income
(I-S) be amount spent

The total amount of $ that she had saved at the end of the year - 12 S

3 times the amount of her monthly take home pay that she did not save. - 3 (I - S)

12 S = 3(I-S)

Solving we get D.

HTH

[gkumar]

Amount saved per month = 1/x * M
where M = monthly pay and 1/x = fraction saved

Amount saved for year = 1/x * M * 12

3 times amount not saved per month = 3 * (1-1/x)*M

Equating yields:
12/x * M = 3 * (1 - 1/x) * M
12/x = 3 * (1 - 1/x)
4/x = 1 - 1/x
5/x = 1
x = 5

so fraction is 1/5

[okigbo]

I have a really tough time with problems like this. Why doesn't plugging in #'s work? I got 1/4 when I plugged in.

[gkumar]

Here's an example of picking numbers:

Since yearly and monthly terms are used, pick numbers that are easy to work with for fraction based numbers for easy arithmetic.

Paycheck per Month: $10
Amount Saved Per Month: 1/x * $10 = $10/x
Amount Not Saved Per Month: $10*(1-1/x) = $10-10/x

Amount saved per year: $10/x*12
3 times Unsaved Amount Per Month: 3*(10-10/x) = 30 - 30/x

Equate them and solve for X:
120/x = 30 - 30/x
150/x = 30
x = 5