SOLUTION: A bus is capable of holding 30 passengers is to be rented for a trip at the rate of $45 per person if 15 or fewer persons go. If more than 15 persons go, each passenger's fare is r

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Question 113354: A bus is capable of holding 30 passengers is to be rented for a trip at the rate of $45 per person if 15 or fewer persons go. If more than 15 persons go, each passenger's fare is reduced by $1.00 for each person over the basic 15. How many passengers does the bus contain if the total fare is $800?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
n = number of passengers
If there were only 15 passengers, The total fare would be
15%2A45+=+675 which is less than 800, so there must have been
more than 15 passengers.
If n = number of passengers, n+-+15 is the number of passengers
over the basic 15. Also, 45+-+%28n+-+15%29 is now the fare per
passenger. The equation is:
Total fare = (fare per passenger)(number of passengers)
800+=+%2845+-+%28n+-+15%29%29%2An
800+=+45n+-+n%5E2+%2B+15n
n%5E2+-+60n+%2B+800+=+0
%28n+-+20%29%28n+-+40%29+=+0
n+=+20 and
n+=+40
Both these answers work if I plug them back into 800+=+%2845+-+%28n+-+15%29%29%2An
so the answer is:
Either 20 or 40 passengers will result in a total fare of $800