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take-home savings

by orel » Wed Nov 26, 2008 5:24 am
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 each month 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 dmateer25 » Wed Nov 26, 2008 6:43 am
Let monthly pay = 10
Let monthly savings =x
monthly pay not saved = (10-x)

Total amount saved in a year will be 12x. This is to be equal to 3 times the amount of the monthly pay that she did not save.

12x = 3(10-x)
12x=30-3x
15x=30
x=2

So she would have saved $2 month.

Now the fraction of her monthly pay that she saved would be 2/10 = 1/5
Last edited by dmateer25 on Wed Nov 26, 2008 10:40 am, edited 1 time in total.
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by orel » Wed Nov 26, 2008 6:47 am
I forgot to use 12 month in an equation when solving...

Dmateer25,
thanks very much!
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by muzali » Wed Nov 26, 2008 9:56 am
dmateer25 wrote:Let monthly pay = 10
Let savings =x
monthly pay not saved = (10-x)

Total amount saved in a year will be 12x. This is to be equal to 3 times the amount of the monthly pay that she did not save.

12x = 3(10-x)
12x=30-3x
15x=30
x=2

So she would have saved $2 month.

Now the fraction of her monthly pay that she saved would be 2/10 = 1/5
Not very clear on this question...total amount saved each month does not imply total amount saved over the course of the year?!
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by dmateer25 » Wed Nov 26, 2008 10:45 am
The question states:
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.
So if her pay is the same each month over the course of the year, and she saves the same fraction of her pay each month.

Then if x=savings in 1 month
12x = saving in 1 year

I'm not sure that answered your question. If not, please let me know what you need explained
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by muzali » Wed Nov 26, 2008 10:56 am
dmateer25 wrote:The question states:
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.
So if her pay is the same each month over the course of the year, and she saves the same fraction of her pay each month.

Then if x=savings in 1 month
12x = saving in 1 year

I'm not sure that answered your question. If not, please let me know what you need explained
It is not clear to me why we need to do 12x. To me, the question states that x=3(10-x) i.e. the fraction saved is equal to 3 times the fraction not saved. Of course, my way of thinking is not giving the right answer, but I am not able to understand how do we know that we ned to take the savings for the entire year to be equal to 3 times the unsaved portion of just one month.
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by dmateer25 » Wed Nov 26, 2008 11:17 am
muzali wrote:
dmateer25 wrote:The question states:
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.
So if her pay is the same each month over the course of the year, and she saves the same fraction of her pay each month.

Then if x=savings in 1 month
12x = saving in 1 year

I'm not sure that answered your question. If not, please let me know what you need explained
It is not clear to me why we need to do 12x. To me, the question states that x=3(10-x) i.e. the fraction saved is equal to 3 times the fraction not saved. Of course, my way of thinking is not giving the right answer, but I am not able to understand how do we know that we ned to take the savings for the entire year to be equal to 3 times the unsaved portion of just one month.
the total amount of money that she saved each month was 3 times
Ahh I see now. You are right, I overlooked this.

I'm going to search google and see if the OA is wrong or the question was worded wrong.
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by dmateer25 » Wed Nov 26, 2008 11:20 am
Found it.

Question worded wrong. It should be:

Alice's take-home pay last year was the same each month and she saved the same fraction of it each month. The total amount of saved money at the end of the year was 3 times the amount of that portion of her monthly take-home money that she did NOT save. If all the money she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

Good catch muzali! I need to be careful what I read!
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by muzali » Wed Nov 26, 2008 12:49 pm
dmateer25 wrote:Found it.

Question worded wrong. It should be:

Alice's take-home pay last year was the same each month and she saved the same fraction of it each month. The total amount of saved money at the end of the year was 3 times the amount of that portion of her monthly take-home money that she did NOT save. If all the money she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

Good catch muzali! I need to be careful what I read!
Thanks for making the effort to clarify this.
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by vittalgmat » Thu Nov 27, 2008 2:47 am
dmateer25 wrote:Let monthly pay = 10
Let monthly savings =x
monthly pay not saved = (10-x)

Total amount saved in a year will be 12x. This is to be equal to 3 times the amount of the monthly pay that she did not save.

12x = 3(10-x)
12x=30-3x
15x=30
x=2

So she would have saved $2 month.

Now the fraction of her monthly pay that she saved would be 2/10 = 1/5
I dint understand how u arrived at
12x = 3(10 -x)
It looks like you are trying to equate the amount of money Alice saved in 1 year with the amount of money she did not save in 1 month.
right ??

Pls clarify.

thanks
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by rohangupta83 » Thu Nov 27, 2008 4:07 am
Alice's monthly pay each month = x
pay saved each month = y
therefore,
pay not saved = x-y

total amount of money saved = 12y
total amount of money saved = 3(x-y) (3 times the amount of money not saved each month)

Hence,

we get:
12y = 3(x-y)
12y = 3x - 3y
15y = 3x
or
y/x = 3/15 (fraction of take home pay saved is take home pay saved/take home pay)
y/x = 1/5
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