Fractions Question

Let's translate this into algebra.

Ysave be Yearly savings
Msave be monthly savings
Mspend be monthly spending

That makes:

Ysave=3Mspend

because Alice's yearly savings are 3 times higher than her MONTHLY spending. Because she saves the same amount each month we can reconstruct the equation as:

12Msave=3Mspend
4Msave=Mspend


In other words, Alice spends 4 times as much as she saves each month. Let's say she spends 4000$ and saves only 1000$, which would fit the equation. Then, for last month, (just as for any other month as well), she saved 1/5 (4000$ out of 5000$) of her total take home pay.

Answer D is correct.

let S be the per month savings...and P be the pay per month.

12S = 3(P-S)

therefore

15S = 3P

thus S/P = 3/15 = 1/5

mdwolman 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 last 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.

Plug in monthly pay = 60. (60 is a good number because it's divisible by all the denominators in the answer choices.)

Answer choice C: 1/4 saved each month
1/4 * 60 = 15 saved each month, 45 not saved.
12*15 = 180 total saved for the whole year.
(Total saved)/(monthly not saved) = 180/45 = 4. We need her to save less.

Answer choice D: 1/5 saved each month
1/5 * 60 = 12 saved each month, 48 not saved.
12*12 = 144 total saved for the whole year.
(Total saved)/(monthly not saved) = 144/48 = 3. Success!

The correct answer is D.