Question

A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? hint: look at the difference between number of people and cost to get cost per person and then cost without people

How much does each person cost?
Write an equation to show cost, c, of a bus with x number of people on it

Answer 1

Base rate: $120

Rate: $2 per person

Equation: f(x)=2x+120

Explanation:

If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40. This means,
`(220-180dollars)/(50-30people)=(40dollars)/(20people)=2(dollars)/(person)`.

These values correspond to a base rate for the bus of $120.

The function for the cost per bus with x number of people on it would be:

`f(x)=2x+100`

This can be checked by using the values given in the problem:

`f(30)=2(30)+120=180\\f(50)=2(50)+120=220`

The base rate of $120 and $2 per person satisfies the given equation and established values.