SOLUTION: A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, the cost per person is greater by $12. What is the cost

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Question 118053: A group can charter a particular aircraft at a fixed total cost. If 36 people
charter the aircraft rather than 40 people, the cost per person is greater by
$12. What is the cost per person if 40 people charter the aircraft?
I can't figure out what the second equation would be?
x= price for 36 ppl.
y= price for 40 ppl.
The first is x=y+12
Thanks a lot for your help
Found 2 solutions by josmiceli, ilana:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think the key to this problem is hidden in the wording of the 1st
sentence. "A group can charter a particular aircraft at a fixed total cost."
I see that as meaning that the cost per person may change, but the
total cost of the trip will end up being the same if there are 36 or
if there are 40 people.
I'll say that c is the cost per person when there are 40
people on the trip. My general equation is
(Total cost of trip) = (number of people)x(cost per person)
So, for 40 people,
C+=+40c
The cost per person when there are 36 people is $12 more, so
C+=+36%28c+%2B+12%29
The total cost is the same in either case, so
40c+=+36%28c+%2B+12%29
40c+=+36c+%2B+432
4c+=+432
c+=+108dollars answer
If they wanted to know the cost per person if there were 36
people the answer would be c+%2B+12
108+%2B+12+=+120dollars

Answer by ilana(307) About Me  (Show Source):
You can put this solution on YOUR website!
So I approached this a little bit differently than you. Instead of trying to form 2 separate equations, I thought about how both groups will pay. We know a group of 40 people is paying the same as a group of 36 people. So each of those 36 people pays $12 more. If there are 40 people each paying $x, the total they pay is 40x. If they each paid x, we know the 36 people each pay $x+12 (your equation), for a total of 36(x+12). We know these totals are equal, so our equation is 40x=36(x+12). Now solve for x to get the amount paid by each of those 40 people. You can check that amount after to make sure the price of the aircraft stays the same for how much the two groups pay.