A question from Prep.

[patrickgong6688]

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?

A1/2
B1/3
C1/4
D1/5
E1/6
I really do not know the why the answer is D.I think the faction of her take home pay she save should be 3/4.

[mithunsam]

Let us see...

Let monthly take home = x
and monthly saving = y

Amount of money Alice saved in an year = 12*y
But the question says that her yearly savings is "3 times the amount of that portion of her monthly take-home pay that she did not save".

That means
12y = 3(x-y) [Monthly take home that she didn't save = Monthly take home - Monthly take home that she saved]

12y = 3x-3y
15y = 3x
x/y = 3/15 [fraction of monthly take that she saved= monthly saved/monthly pay]
x/y = 1/5

Answer D

[patrickgong6688]

I understand! Thank you.The problem for me is that i did not read the question very carefully. I had thought that it was 12y=3*12*(x-y).thank you!

[jnelson0612]

Great!