SOLUTION: A group of students want to rent a car to sightseeing by share the rental cost. If the group has 12 people less each people will have to pay 18 dollars more, And If the group has e

Question 387355: A group of students want to rent a car to sightseeing by share the rental cost. If the group has 12 people less each people will have to pay 18 dollars more, And If the group has eight people more each people will have to pay 6 dollars less. How much is the rental cost?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let C = rental cost, and n = the # of students. Then from the 2nd sentence, we get
(1)
and from the 3rd sentence, we get
. (2)
From (1) we get (3),
and from (2), . (4)
Then 2C = 3n(n-12) (5)
from (3), and
4C = 3n(n+8) (6),
from (4).
By combining (5) and (6), we get
6n(n-12) = 3n(n+8), or
2(n-12) = n+8, after canceling 3n. Then
2n - 24 = n+8, or
n = 32, the # of students.
This rental cost, use (5):
2C = 3*32*20, or C = $960.

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