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 timex 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?
1/2
1/3
1/4
1/5
1/6
d
Word Problem
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Here's an algebraic approach.outty 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 timex 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
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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We can PLUG IN THE ANSWERS, which represent the fraction that must be saved each month.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
When the correct answer choice is plugged in, the total amount saved at the end of the year will be 3 times the amount NOT saved each month.
Answer choice D: 1/5
Let the monthly pay = $5.
Since 1/5 is saved each month, the amount saved each month = 1/5 * 5 = $1.
Thus, the amount NOT saved each month = 5-1 = $4.
Since $1 is saved each month, the total amount saved at the end of the year = 12*1 = $12.
Success!
The total amount saved at the end of the year ($12) is 3 times the amount not saved each month ($4).
The correct answer is D.
Slightly different algebraic approach:
Let the monthly income = $1.
Let x = the fraction saved each month.
Fraction not saved each month = 1-x.
Total saved at the end of the year = 12x.
Since the total saved 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.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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