Math CentralQuandaries & Queries


Question from Heather:

On the bus question you answered, what would be the fixed rate? Is that the rate per person or is that also the base rate? ( cost of empty bus)?

Hi Heather,

The question Stephen solved in the page you reference was

Problem: 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? How much does each person cost? Show this using y = mx + b form.

Stephen's solution began

Let x = the number of people on the bus
Let y = the total cost for the bus with its passengers to use the ferry.

and he arrived at the answer

\[y = 2x + 120.\]

In this expression if $x = 0,$ that is there are no passengers then the cost is $\$120$ so the cost for an empty bus to use the ferry is $\$120.$ If $x = 1$ then the cost is $120 + 2 = 122$ dollars and if $x = 2$ then the cost is $120 + 4 = 124$ dollars and so on. The number 2 in the equation $y = 2x + 120$ is the additional cost per person in dollars. Thus the "fixed" cost is $\$120,$ fixed because it doesn't depend on the number of passengers and $\$2$ is the additional cost per person.

I hope this helps,

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