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Help! Word Problem - Fractions

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by britney89 » Mon Oct 06, 2014 4:29 pm
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: D

Maybe I'm setting up my algebraic equations wrong, but I got 1/2. Any tips/strategies to answer this questions will be very helpful.

Thanks!
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by [email protected] » Mon Oct 06, 2014 5:23 pm
Hi britney89,

The wording of this question requires that we pay very careful attention to the details and correctly "translate" the text into math.

We're told that Alice has the same take-home pay every month and that she saves the same fraction of her pay every month...

Each Month:

X = take-home pay
V = money saved
X-V = money spent

Next we're told that the total money saved for THE YEAR was 3 TIMES the amount that she did NOT save EACH MONTH.

Total saved for the YEAR = 12(V)
Amount she did not save each MONTH = X-V

12V = 3(X-V)
12V = 3X - 3V
15V = 3X
5V = X

We're asked what fraction of her take home pay (X) did she save each money (V) --> so we're looking for V/X

5V = X
5V/X = 1
V/X = 1/5

Final Answer: D

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Rich
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by Brent@GMATPrepNow » Mon Oct 06, 2014 5:59 pm
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 saved at the end of the year was 3 times the amount of her take-home pay that she didn't save. If all money she saved lasr year was from her take-home pay, what fraction of her pay did she save each month?

a)1/2
b)1/3
c)1/4
d)1/5
e)1/6
Here's an another approach.

Let M = Alice's monthly take home pay
Let f = the fraction we'll use to calculate monthly savings
The means that fM = the amount of $ Alice saves EACH MONTH.
And this means that her ANNUAL savings = 12fM

Important: If f = the fraction used to calculate monthly savings, then 1-f = the fraction used to calculate amount not saved
The means that (1-f)M = the amount of $ Alice does not save each month.

Now we're ready to write an equation.

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.
We get: 12fM = 3(1-f)M
Now solve for f
Expand to get: 12fM = 3M - 3fM
Simplify: 15fM = 3M
Divide both sides by 15M to get: f = 3M/15M = [spoiler]1/5 = D[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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