neeti2711 wrote: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?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
We can plug in the answers, which represent the fraction saved each month.
Answer choice C: 1/4
Let the total monthly pay = 4.
Amount saved each month = 1/4 * 4 = 1.
Amount saved for the whole year = 12*1 = 12.
3 times the amount not saved each month = 3*3 = 9.
Since these last two values must be equal, too much money is being saved.
Eliminate A, B and C.
Answer choice D: 1/5
Let the total monthly pay = 5.
Amount saved each month = 1/5 * 5 = 1.
Amount saved for the whole year = 12*1 = 12.
3 times the amount not saved each month = 3*4 = 12.
Success!
The correct answer is
D.
Algebraically:
Let the fraction saved each month = x.
Amount saved for the whole year = 12x.
Fraction not saved each month = 1-x.
Since the amount saved for the whole year is equal to 3 times the fraction not saved each month, we get:
12x = 3(1-x)
12x = 3 - 3x
15x = 3
x = 3/15 = 1/5.
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