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# A group of college friends plan to rent a house together for x dollars

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Joined: 02 Sep 2009
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A group of college friends plan to rent a house together for x dollars [#permalink]

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17 Feb 2016, 04:34
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Difficulty:

5% (low)

Question Stats:

91% (00:53) correct 9% (00:47) wrong based on 55 sessions

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A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If five, rather than eight people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?

A. x/3

B. x/5

C. x/8

D. 3x/20

E. 3x/40

Kudos for correct solution.
[Reveal] Spoiler: OA

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Re: A group of college friends plan to rent a house together for x dollars [#permalink]

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20 Feb 2016, 04:39
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Bunuel wrote:
A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If five, rather than eight people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?

A. x/3

B. x/5

C. x/8

D. 3x/20

E. 3x/40

Kudos for correct solution.

consider rent amount X=400

If 5......... rent/person=80

If 8..........rent/person=50

Difference =30

Choice D.........3*400/20= 60

choice E ......30

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Re: A group of college friends plan to rent a house together for x dollars [#permalink]

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12 Sep 2017, 10:12
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A group of college friends plan to rent a house together for x dollars [#permalink]

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13 Sep 2017, 08:51
Bunuel wrote:
A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If five, rather than eight people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?

A. x/3

B. x/5

C. x/8

D. 3x/20

E. 3x/40

Kudos for correct solution.

Picking numbers is probably faster (where x is a multiple of 5 and 8), but algebraically:

(Total cost)/(# of persons) = cost per person

Cost per person with 8 persons, where total cost is x, is $$\frac{x}{8}$$

If 5 persons, then cost per person is $$\frac{x}{5}$$

The difference in cost per person is (choose the smaller fraction to subtract)

$$\frac{x}{5}$$ - $$\frac{x}{8}$$ =

$$\frac{(8x-5x)}{40}$$ = $$\frac{3x}{40}$$

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Re: A group of college friends plan to rent a house together for x dollars [#permalink]

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13 Sep 2017, 14:00
Expert's post
Top Contributor
Bunuel wrote:
A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If five, rather than eight people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?

A. x/3

B. x/5

C. x/8

D. 3x/20

E. 3x/40

Kudos for correct solution.

Cost per person = (TOTAL cost)/(number of people)

Cost per person with 8 people
Cost per person = x/8

Cost per person with 5 people
Cost per person = x/5

If five, rather than eight people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?
difference = x/5 - x/8 ...check the answer choices - not there.
Looks like they want us to simplify x/5 - x/8

Find a common denominator of 40 to get: x/5 - x/8 = 8x/40 - 5x/40
= 3x/40

[Reveal] Spoiler:
E

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Re: A group of college friends plan to rent a house together for x dollars [#permalink]

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15 Sep 2017, 10:14
Bunuel wrote:
A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If five, rather than eight people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?

A. x/3

B. x/5

C. x/8

D. 3x/20

E. 3x/40

The cost per person when 8 people rent the house is x/8 and the cost per person when 5 people rent the house is x/5; thus, when five people rent the house, each of them will have to pay x/5 - x/8 = 8x/40 - 5x/40 = 3x/40 dollars more.

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Jeffery Miller

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Re: A group of college friends plan to rent a house together for x dollars   [#permalink] 15 Sep 2017, 10:14
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