Problem Solving

Cant figure out what approach to take with this one. Tried it algebraically, got too lengthy and couldn't decide what numbers to pick !


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. What fraction of her take home pay did she save each month.

Answer is [spoiler] 1/5 [/spoiler]

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 the 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?

1/2
1/3
1/4
1/5
1/6

We can plug in the answers, which represent the fraction saved each month.

Answer choice C: 1/4
Let the monthly pay = 4.
Amount saved each month = (1/4)4 = 1, so the amount not saved each month = 3.
Amount saved over the whole year = 12*1 = 12.
(Total saved)/(monthly not saved) = 12/3 = 4.
Since it is required that (total saved)/(monthly not saved) = 3, too high a fraction is being saved.
Eliminate A, B and C.

Answer choice D: 1/5
Let the monthly pay = 5.
Amount saved each month = (1/5)5 = 1, so the amount not saved each month = 4.
Amount saved over the whole year = 12*1 = 12.
(Total saved)/(monthly not saved) = 12/4 = 3.
Success!

The correct answer is D.