Algebraic Word Problem

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Algebraic Word Problem

by me_1234 » Tue Dec 09, 2014 5:20 pm
I'd like to check if my understanding for below question is correct, or if there is a better way to do this.

I wrote down equations where x is total monthly pay

Total saved = (12 * y)x, where y = total saved per month

Kept per month = k

12y = 3k

4y=k

4+1 = 5, so she saved 1/5 each month (answer D)

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

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by [email protected] » Tue Dec 09, 2014 5:36 pm
Hi melanie.espeland,

Yes, your logic/approach is correct. Here is a link to a discussion of this question, with various approaches from the Experts here:

https://www.beatthegmat.com/word-problems-t270244.html

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by Brent@GMATPrepNow » Tue Dec 09, 2014 10:16 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
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by me_1234 » Wed Dec 10, 2014 10:02 am
Thanks all