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Lisa spends 3/8th of her salary on rent and 5/12 on food. He

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Lisa spends 3/8th of her salary on rent and 5/12 on food. He [#permalink]

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Lisa spends 3/8th of her salary on rent and 5/12 on food. Her roommate, Carrie earns about twice as much as Lisa, spends 1/4th of her salary on the rent and 1/2 on food. If the two women decide to contribute the rest of their salary to charity every month, what fraction of their combined monthly income will they donate.

Hi all!!! Have a small query on a ratio problem. Though it's a relatively simple question, couldn't arrive at the desired solution. it would be great if any of you could help me with this. Thanks in advance :)


The answer given is
[Reveal] Spoiler:
17/72
but what I derived is 17/24.

Here are the steps I've followed, please correct me on this note.

x = lisa's salary from which, 3/8x=rent ; 5/12x=food ; remaining towards charity= x- 3/8x-5/12x= 5x/24;
y=Carrie's salary; 1/4y=rent;1/2y=food; charity= y-1/4y-1/2y= 1/4y

but, y=2x ( Carrie's salary twice as much as Lisa's)

Hence Carries contribution to charity= 1/4y = 1/4 *2x= 1/2x

Their combined contribution to charity = 1/2x+ 5/24x = 17/24x

Hence the desired answer is 17/24.

But , the correct answer is
[Reveal] Spoiler:
17/72




Kindly, help!!! :?

Sandhya Iyer

Originally posted by SandhyaIyer on 27 Jun 2014, 09:45.
Last edited by Bunuel on 27 Jun 2014, 10:47, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Lisa spends 3/8th of her salary on rent and 5/12 on food. He [#permalink]

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New post 27 Jun 2014, 10:58
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SandhyaIyer wrote:
Lisa spends 3/8th of her salary on rent and 5/12 on food. Her roommate, Carrie earns about twice as much as Lisa, spends 1/4th of her salary on the rent and 1/2 on food. If the two women decide to contribute the rest of their salary to charity every month, what fraction of their combined monthly income will they donate.

Hi all!!! Have a small query on a ratio problem. Though it's a relatively simple question, couldn't arrive at the desired solution. it would be great if any of you could help me with this. Thanks in advance :)


The answer given is
[Reveal] Spoiler:
17/72
but what I derived is 17/24.

Here are the steps I've followed, please correct me on this note.

x = lisa's salary from which, 3/8x=rent ; 5/12x=food ; remaining towards charity= x- 3/8x-5/12x= 5x/24;
y=Carrie's salary; 1/4y=rent;1/2y=food; charity= y-1/4y-1/2y= 1/4y

but, y=2x ( Carrie's salary twice as much as Lisa's)

Hence Carries contribution to charity= 1/4y = 1/4 *2x= 1/2x

Their combined contribution to charity = 1/2x+ 5/24x = 17/24x

Hence the desired answer is 17/24.

But , the correct answer is
[Reveal] Spoiler:
17/72




Kindly, help!!! :?

Sandhya Iyer


The question asks about the fraction of their combined salary that they donated. Their combined salary is x + y = x + 2x = 3x. So, if they donate 17/24 of x, then they donate 17/72 of 3x.

You could solve in another way:

Let Lisa's salary be $24 and Carrie's salary be twice of that, so $48.

Lisa donates 24 - (3/8*24 + 5/12*24) = $5.
Carry donates 48 - (1/4*48 + 1/2*48) = $12.

So, together they donate (5 + 12)/(24 + 48) = 17/72 of their combined salary.

Hope it's clear.
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Re: Lisa spends 3/8th of her salary on rent and 5/12 on food. He [#permalink]

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New post 27 Jun 2014, 22:53
Yes, so we have to find the fraction of the amount contributed on the whole.


Thank you :)


Sandhya Iyer
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Re: Lisa spends 3/8th of her salary on rent and 5/12 on food. He [#permalink]

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New post 11 Dec 2017, 12:36
SandhyaIyer wrote:
Lisa spends 3/8th of her salary on rent and 5/12 on food. Her roommate, Carrie earns about twice as much as Lisa, spends 1/4th of her salary on the rent and 1/2 on food. If the two women decide to contribute the rest of their salary to charity every month, what fraction of their combined monthly income will they donate.


We can let p = Lisa’s monthly paycheck. Thus, Carrie’s monthly paycheck = 2p. Now we can determine each person’s rent expense, food expense, and remaining money in terms of p.

Lisa:

Rent = (3/8)p

Food = (5/12)p

Remainder = p - (3/8)p - (5/12)p = (24/24)p - (9/24)p - (10/24)p = (5/24)p

Carrie:

Rent = (1/4)(2p) = (1/2)p

Food = (1/2)(2p) = p

Remainder = 2p - (1/2)p - p = (1/2)p

From the above, we see that the combined money they donate to charity is the sum of their remaining money:

(5/24)p + (1/2)p = (5/24)p + (12/24)p = (17/24)p

Also, the combined money they earn in a month is p + 2p = 3p.

Thus, the fraction of their monthly income donated to charity is [(17/24)p]/(3p) = (17/24)/3 = 17/72.
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Re: Lisa spends 3/8th of her salary on rent and 5/12 on food. He [#permalink]

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New post 12 Dec 2017, 02:49
SandhyaIyer wrote:
Lisa spends 3/8th of her salary on rent and 5/12 on food. Her roommate, Carrie earns about twice as much as Lisa, spends 1/4th of her salary on the rent and 1/2 on food. If the two women decide to contribute the rest of their salary to charity every month, what fraction of their combined monthly income will they donate.

Sandhya Iyer


Let Lisa's salary be x , So, Carrie's salary will be 2x. Total monthly income = x + 2x = 3x.
Rent of Lisa = 3/8 x , Food of Lisa = 5/12 x . Total spent = (3/8 +5/12)x = 19/24 x. Left amount = 5/24 x
Rent of Carrie = 1/4 x , Food of Carrie = 1/2 x. Total spent = (1/4 + 1/2 )x = 3/2 x. Left amount = 1/2 x

Total Spent = 5/24 x + 1/2 x = 17/24 x

Fraction of combined monthly income they donate = 17/24 x / 3x = 17/72
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Re: Lisa spends 3/8th of her salary on rent and 5/12 on food. He [#permalink]

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New post 12 Dec 2017, 08:21
SandhyaIyer wrote:
Lisa spends 3/8th of her salary on rent and 5/12 on food. Her roommate, Carrie earns about twice as much as Lisa, spends 1/4th of her salary on the rent and 1/2 on food. If the two women decide to contribute the rest of their salary to charity every month, what fraction of their combined monthly income will they donate.


Let Lisa's salary be 96
Amount spent on Rent is 36
Amount spent on Food is 40
Amount saved is 20

Let Carrie's salary be 192
Amount spent on Rent is 48
Amount spent on Food is 96
Amount saved is 48

Total salary of the 2 women is 96 + 192 = 288
Total amount saved (Contributed to charity) is 20 + 48 = 68

So, fraction of their combined monthly income will they donate is 68/288 = 17/72 (Answer)

Hope this helps.
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Re: Lisa spends 3/8th of her salary on rent and 5/12 on food. He   [#permalink] 12 Dec 2017, 08:21
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