Expert: Ahmed Salami - 10/19/2004

Question
Would you please take me through the steps to solve the following question? I thank you very much.

**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. What is the cost per person if 40 people charter the aircraft?**

Answer
Hi Naomi,
Well, what the information is telling us is that it doesn't matter what the number of people in a group is, the total amount paid by the group to charter the aircraft is always fixed. Now, when 36 people pay exactly the same amount as 40 people have for the same thing, its obvious that each person in the 40 people group has paid less than a counterpart in the 36 people group.
Now to the maths.
Let's assign this fixed cost as C. For 36 people, the price per person in simply C/36 while we have C/40 per person for the 40 people group.
But the question says that the difference in the cost per person for the two groups is $12. Therefore,
C/36 - C/40 = 12
multiplying boh sides by 360, we have
(360)C/36 - (360)C/40 = (360)12
10C - 9C = 4320
C = $4320
But the question requires the cost per person for the 40 people group
= C/40
= 4320/40
= $108
I hope you understand it.
Regards.