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Alice's take-home pay last year was the exact same each

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Alice's take-home pay last year was the exact same each [#permalink] New post 12 Apr 2008, 12:38
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Alice's take-home pay last year was the exact 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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Re: Fractions [#permalink] New post 12 Apr 2008, 13:27
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Hi,

I think it’s D. Here’s the solution:

Let x be the fraction of her monthly saved money (then (1-x), consequently, is the fraction corresponding to NOT-saved money), and a – the monthly pay itself. Amount of her saved money during 12 months is 12*x*a, and, since it’s trice the number of the money she did not save in one month, we obtain:

12*x*a = 3*(1-x)*a, and, consequently, 4x=1-x and x=1/5.
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Re: Fractions [#permalink] New post 22 Jan 2010, 11:05
yeah. I got D too.

x-y=1 where y is amount saved per month

also 12y = 3x; that is 12 times the monthly amount saved equals 3 times the amount not saved in a given month

do the math and

x=4y so 80% was not saved and 20% was saved.
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Re: Fractions [#permalink] New post 23 Jan 2010, 10:19
I got the answer as C

I solve it by picking numbers

let x (takehome pay) = 12
and fraction saved be 12(1/4) = 3

so at the end of year she saved =3*12=36
amount of money she did not saved = 9*12=108

which satisfies the criteria
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

so the fraction must be 1/4 and the ans is C
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Re: Fractions [#permalink] New post 23 Jan 2010, 11:30
Maybe I'm stupid but if

Quote:
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.


And she did not save 9 per month where she received 12 then 3x9=27 but according to your calculation she saved 36 and not 27. that means C can't be the answer unless i'm completely wrong.
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Re: Fractions [#permalink] New post 23 Jan 2010, 12:36
vannbj wrote:
Maybe I'm stupid but if

Quote:
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.


And she did not save 9 per month where she received 12 then 3x9=27 but according to your calculation she saved 36 and not 27. that means C can't be the answer unless i'm completely wrong.





alice's every month take home pay = 12 (just picking random suitable number)
alice saves per month=12*(1/4)=3
alice does not save per month = 9

1 year =12 months
so for the whole year she save = 3*12=36
so for the whole year alice didnot save =9*12 =108
Re: Fractions   [#permalink] 23 Jan 2010, 12:36
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Alice's take-home pay last year was the exact same each

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