SOLUTION: You want to take your class in a field trip to the field museum in Chicago. The total cost of the trip will include the fixed fee for the bus; each person must pay an admission fee

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: You want to take your class in a field trip to the field museum in Chicago. The total cost of the trip will include the fixed fee for the bus; each person must pay an admission fee      Log On


   

Question 1002271: You want to take your class in a field trip to the field museum in Chicago. The total cost of the trip will include the fixed fee for the bus; each person must pay an admission fee to enter the museum. To take 10 people on the trip, it will cost $1400; to take 15 people it will cost $1475. For 20 people it would cost $1550.
A. Find the bus fee
B. Find a formula that gives the cost of the field trip, C, in terms of the number of people,p, on the trip.
C. You get a donation of $1800 to pay for expenses for this trip. How many people can you bring?
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
The description gives points (p,C):
(10,1400), (15,1475), (20,1550).

Slopes among the successive points are
%281475-1400%29%2F%2815-5%29=15
and
%281550-1475%29%2F%2820-15%29=15
both slopes being the same, 15.
The points have a linear fit.

Picking the first data point and using point-slope form,
C-1400=15%28p-10%29
C-1400=15p-150
C=15p-150%2B1400
highlight%28C=15p%2B1250%29------Formula for cost as a function of how many attend.

The bus cost by itself is $1250.

The last question means 15p%2B1400=1800, and you want to solve for the value of p.