Question

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

Answer 1

d) 1/5

Explanation:

If we call x the amount of take-home pay each month and we call y the amount of savings for each month:

The total amount of money she saved at the end of the year (after 12 months) is: 12y

The monthly take-home pay that she didn't save is: x - y

The problem tells us that 12y is three times the amount she didn't save, therefore:

12y = 3(x-y)

`12y=3(x-y)\\12y=3x-3y\\15y=3x\\y=3x/15\\y=x/5\\y=(1)/(5)x`

Therefore, she saved 1/5 of her take-home pay each month.