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

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04 Jul 2006, 08:05

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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?

11. 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) 6x (B) 10x (C) 16x (D) 403x (E) 803x

I solved it by plugging in numbers. But I'd like to see some one do it without plugging.

11. 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/16 (C) x/40 (D) 3x/40 (E) 3x/80

I solved it by plugging in numbers. But I'd like to see some one do it without plugging.

Choose x as a multiple of 16, I chose 64:

So for 10 people, that's 6.4 each and for 16 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is E.

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

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16 Jan 2016, 06:35

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

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16 Jan 2016, 06:38

Just plugging in values

X= 160 Cost per person if we consider 10 = 16 Cost per person if we consider 16 = 10 Difference between costs is 6 dollars. Plugging in the value of x into the answer choices, let's see which one yields a result of 6. And that is E.

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/16 (C) x/40 (D) 3x/40 (E) 3x/80

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

Cost per person with 16 people Cost per person = x/16

Cost per person with 10 people Cost per person = x/10

How many more dollars, in terms of x, will it cost per person? difference = x/10 - x/16 ...check the answer choices - not there. Looks like they want us to simplify x/10 - x/16

Find a common denominator of 80 to get: x/10 - x/16 = 8x/80 + 5x/80 = 13x/80

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/16 (C) x/40 (D) 3x/40 (E) 3x/80

It will cost x/10 dollars per person when 10 people split the cost and x/16 dollars when 16 people split the cost. Thus, it will cost x/10 - x/16 = 8x/80 - 5x/80= 3x/80 dollars more when 10 people split the cost versus when 16 people do.

Answer: E
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