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Alice’s take-home pay last year was the same each month, and
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09 Jun 2020, 09:15
09 Jun 2020, 09:15
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65% (02:27) correct
34% (02:47) wrong based on 46 sessions
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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
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6
Re: Alice’s take-home pay last year was the same each month, and
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09 Jun 2020, 09:15
09 Jun 2020, 09:15
1
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Re: Alice’s take-home pay last year was the same each month, and
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09 Jun 2020, 09:45
09 Jun 2020, 09:45
2
Carcass 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 each month?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6
Here's one 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 = 1/5
Answer: D
Cheers,
Brent
