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08 Jun 2020, 00:17
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changhiskhan
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
The variables are : A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6
alice's take home pay per month: p
her savings per month : s
total amount saved that year : t
monthly take home pay she did not save: n
question:
s/p=?
The relationships:
n=p-s
t=12s
t=3n
t=3n =>12s=3(p-s)
15s=3p
s/p=1/5
06 Sep 2020, 23:35
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If we read in one go, we realize that there's a lot of data it might get confusing.
Break it into parts
(1) Alice’s take-home pay last year was the same each month. Let this be = x
(2) She saved the same fraction of her take-home pay each month. Let this be = y
(3) The total amount of money that she had saved at the end of the year = 12y
(4) was 3 times the amount of that portion of her monthly take-home pay that she did NOT save.
Amount not saved every month = amount spent every month = earned - saved = x - y
Therefore 12y = 3(x - y)
12y = 3x - 3y
3x = 15y
x = 5y
(5) 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?
Basically what is \(\frac{y}{x} = \frac{y}{5y} = \frac{1}{5}\)
Option D
Arun Kumar
Break it into parts
(1) Alice’s take-home pay last year was the same each month. Let this be = x
(2) She saved the same fraction of her take-home pay each month. Let this be = y
(3) The total amount of money that she had saved at the end of the year = 12y
(4) was 3 times the amount of that portion of her monthly take-home pay that she did NOT save.
Amount not saved every month = amount spent every month = earned - saved = x - y
Therefore 12y = 3(x - y)
12y = 3x - 3y
3x = 15y
x = 5y
(5) 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?
Basically what is \(\frac{y}{x} = \frac{y}{5y} = \frac{1}{5}\)
Option D
Arun Kumar
16 Apr 2021, 11:30
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Quote:
Let Alice's monthly take-home pay be \(p\) and her monthly savings be \(s\). Total savings will be \(12s\) and we know that this is 3 times the amount she spends in month which is: \(p-s\). So we have:
\(12s=3(p-s)\) --> \(s=p\frac{1}{5}\)
Answer: D.
Hi Bunuel , just a little tweak. I had the same equation, except:
if 12s is the saving for the entire year, then P-12s is the expenditure the entire year, so my equation looked like this:
12s= 3(p-12s). why are we taking the saving/month on the RHS, rather than the saving that entire year?
thanks, in advance
