# GRE Algebra question

1. A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12. (a) What is the fixed total cost to charter the aircraft? (b) What is the cost per person if 40 people charter the aircraft? ans: 15. (a)$\$$4,320 (b) \$$108

Can the answers be found with the information provided in the question? If yes , how?

As far as I understand the question, my approach to the question is as follows: for 40 people, cost per person be x for 36 people, cost per person is x+12 so for 40 people, total cost is 40x for 36 people, total cost is 36(x+12)

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Put $\,x=\,$ the fixed cost, then we're said, exactly as you wrote down:

$$40x=36(x+12)\Longrightarrow 4x=36\cdot 12\Longrightarrow\;\; (b)\;\;x=108$$

With this you can do the rest.

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Impossible, as then we get $\,x\,$ negative. – DonAntonio Sep 7 '12 at 2:55
@sonam make sure you check your math first before you comment that someone else is wrong. its polite. – yiyi Sep 7 '12 at 2:57
thanks my mistake sorry – pradip Sep 7 '12 at 2:59

Rather than equations, Quantitative reasoning is expected more in GRE. Though both of them follow the same path.

The reasoning here is as 4 people are not chartering their expenses are to be bore by the remaining 36 people. So, the expense of each of those 4 opted out people are bore by 36/4=9 of the remaining travellers. So, each of those opted out candidates has an expense of 12*9=108 This is the cost per person when 40 people are chartering Total expenditure is total travellers that is 40 multiplied by expenditure per personn that is 108, this gives 4320

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a. If the total fixed cost is $C$, then the cost per person is $$\frac{C}{36} = \frac{C}{40} + 12 \Rightarrow C = 12\left(\frac{1}{36}-\frac{1}{40}\right)^{-1}$$ b. C/40

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does your ans match with the answer given above, dont think so – pradip Sep 7 '12 at 2:35
@sonam It does match. – anon Sep 7 '12 at 2:51
@sonam you were asking the question, which implies that you don't know how to solve it. It could be considered rude to tell those that gave you answers, that they are wrong. If you know that their answer is wrong, then that means you understand how to solve the problem, thus you should not be asking for help. – yiyi Sep 7 '12 at 2:59
i didnot know previously, looking at the answers given, gave me clue to solve it – pradip Sep 7 '12 at 3:01
Google 12/(1/36-1/40) and (12/40)/(1/36-1/40) and you'll see that my solution gives the right answer. – Eric Angle Sep 7 '12 at 3:12