For a field trip, a bus company charges a flat fee plus an additional fee per student. For 30 students, the total cost is $130. If there are 45 students, the total cost is $160.

Question

For a field trip, a bus company charges a flat fee plus an additional fee per student. For 30 students, the total cost is $130. If there are 45 students, the total cost is $160.

Answer 1

I assume you're looking to find the per-student charge and the flat fee.

You can set up a system of equations;

x = per-student fee; F = flat fee.

30x + F = $130

45x + F = $160 Substract to eliminate the flat fee term.

-15x = -30, so x = $2.00 per student.

30(2) + F = 130

F = 130 - 60 = $70 flat fee.

You may have been able to figure this out with no algebra. 15 more students added $30 to the total cost, so each student must have been charged $2.

With that info you can figure out that the flat fee is the difference between the total variable cost based on the number of students and the total cost.