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# The cost to rent a small bus for a trip is x dollars, which

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The cost to rent a small bus for a trip is x dollars, which [#permalink]

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03 Mar 2014, 01:28
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of x, will it cost per person?

(A) x/6
(B) x/10
(C) x/16
(D) 3x/40
(E) 3x/80

Problem Solving
Question: 124
Category: Algebra Applied problems
Page: 77
Difficulty: 600

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Re: The cost to rent a small bus for a trip is x dollars, which [#permalink]

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03 Mar 2014, 01:28
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SOLUTION

The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of x, will it cost per person?

(A) x/6
(B) x/10
(C) x/16
(D) 3x/40
(E) 3x/80

For 16 people, the cost per person = x/16;
For 10 people, the cost per person = x/10;

The difference = x/10 - x/16 = 3x/80.

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The cost to rent a small bus for a trip is x dollars, which [#permalink]

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Updated on: 08 Aug 2014, 03:08
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Answer = (E) $$\frac{3x}{80}$$

When 16 people are decided to go, cost per person $$= \frac{x}{16}$$ .............. (1)

However, after this, only 10 people go. So cost of 6 has to be shared between them.

From (1)..... cost for 6 people $$= 6 * \frac{x}{16}$$

$$\frac{6x}{16}$$ has to be shared among the remaining 10, so $$\frac{6x}{(16*10)}$$

Answer $$= \frac{3x}{80}$$
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Originally posted by PareshGmat on 03 Mar 2014, 02:53.
Last edited by PareshGmat on 08 Aug 2014, 03:08, edited 1 time in total.
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Re: The cost to rent a small bus for a trip is x dollars, which [#permalink]

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03 Mar 2014, 02:58
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One more method, say x = 80

When 16 people were to go, it was 5 $per person 6 people dropped off (6*5) = 30 $$These 30$$ are to be shared with the remaining 10, so per person = 3$ additional burden
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Re: The cost to rent a small bus for a trip is x dollars, which [#permalink]

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04 Mar 2014, 03:21
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One more Method:

Initial Cost = x/16

New Cost Incurred = x/10

So the cost per person to be paid extra = New Cost- Old Cost

x/10 - x/16 = 3x/80

Option E
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Re: The cost to rent a small bus for a trip is x dollars, which [#permalink]

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08 Mar 2014, 11:49
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SOLUTION

The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of x, will it cost per person?

(A) x/6
(B) x/10
(C) x/16
(D) 3x/40
(E) 3x/80

For 16 people, the cost per person = x/16;
For 10 people, the cost per person = x/10;

The difference = x/10 - x/16 = 3x/80.

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Re: The cost to rent a small bus for a trip is x dollars, which [#permalink]

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11 Jun 2014, 14:52
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Let X be 80: 80/10=8 and 80/16=5 the difference is 8-5=3
Plugin 80 for X in the answer choices the result must equal to 3 you can quickly see that E is the right answer: (3*80)/80=3
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Re: The cost to rent a small bus for a trip is x dollars, which [#permalink]

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12 Sep 2015, 13:19
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BrainLab wrote:
Let X be 80: 80/10=8 and 80/16=5 the difference is 8-5=3
Plugin 80 for X in the answer choices the result must equal to 3 you can quickly see that E is the right answer: (3*80)/80=3

TAKE LCM OF 10 AND 16 IT WILL COME OUT TO 80 ...NOW TAKE X AS 80 ....
PUT VALUES IN THE ABOVE EQUATION .. I THINK THIS IS THE SIMPLEST APPROACH

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Re: The cost to rent a small bus for a trip is x dollars, which [#permalink]

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24 Aug 2017, 00:52
More people, the less you spend.

Question asks "how many more dollars, in terms of x". Meaning you have to subtract the lesser value from the more value.

1. x / 16 - x/10
2. Create equal denominators ---> 10x / 160 - 16x/160 ---> swap the position of the fraction so no negative ---> 16x/160 - 10x/160 = 6x/160 = 3x/80

Therefore (E) 3x / 80
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Re: The cost to rent a small bus for a trip is x dollars, which [#permalink]

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29 Aug 2017, 17:18
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of x, will it cost per person?

(A) x/6
(B) x/10
(C) x/16
(D) 3x/40
(E) 3x/80

The cost per person is x/10 if 10 people share the ride. Similarly, the cost per person is x/16 if 16 people share the ride. Thus, the difference is:

x/10 - x/16 = 8x/80 - 5x/80 = 3x/80

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Re: The cost to rent a small bus for a trip is x dollars, which   [#permalink] 29 Aug 2017, 17:18
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