SOLUTION: I am having problems with this word problem: A group can charter a particular aircraft at a total fixed cost. If 36 people charter the aircraft rather than 40 people, then the cos

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Question 214725This question is from textbook Practicing to Take the GRE General Test
: I am having problems with this word problem:
A group can charter a particular aircraft at a total fixed 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?
I have defined the cost if 40 people charter as x and the cost if 36 people charter as y.
The only equation I can come up with so far is 36y=40(x+12), but I know I need some other equation if I want to solve for either variable.
The back of the book states the answer as 108, but I cannot figure out how to get there.
Thanks in advance for your help! This question is from textbook Practicing to Take the GRE General Test

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let

x=cost per person (for 40 people) in dollars
y=total cost in dollars


If 40 people attend, then the cost per person 'x' is simply the total cost 'y' divided by the number of people going (40). In other words, x=y%2F40 (eg: if the total cost is $80, then the cost per person is 80%2F40=2 dollars). This is your first equation.


Now if 36 people attend instead of 40, the cost per person will increase by $12. So this means that the new cost per person is x%2B12 if 36 people go. This is equal to y%2F36 (since the total cost is now divided among 36 people). So x%2B12=y%2F36. This is the second equation.


x%2B12=y%2F36 Start with the second equation.


y%2F40%2B12=y%2F36 Plug in x=y%2F40


360%28y%2Fcross%2840%29%29%2B360%2812%29=360%28y%2Fcross%2836%29%29 Multiply EVERY term by the LCD 360 to clear out the fractions.


9y%2B4320=10y Multiply and simplify.


9y=10y-4320 Subtract 4320 from both sides.


9y-10y=-4320 Subtract 10y from both sides.


-y=-4320 Combine like terms on the left side.


y=%28-4320%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=4320 Reduce.


Since 'y' is the total cost, this means that the total cost is $4,320


x=y%2F40 Move back to the first equation.


x=4320%2F40 Plug in y=4320


x=108 Divide


Since 'x' is the cost per person when 40 people were going, this means that the cost per person for 40 people is $108.