GRE Algebra question

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)

Answer 1

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.

Answer 2

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