Question

A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32. How much do you think a bus containing 30 people would be charged?

Answer 1

The cost of a bus containing 30 people is $98.

Step-by-step explanation:

Step 1:

Assume the cost per person is x.

The cost parking charges consist of a base charge and then a charge which depends on the number of people in a vehicle.

To determine the cost per person we divide the difference between two cases by the difference in the number of people in the car.

In case 1, the cost for 2 people is $14. In case 2, the cost for 4 people is $20.

The cost per person, x $= \frac{20-14}{4-2} = \frac{6}{2} = 3.$

So for each person, the cost is $3.

Step 2:

If there are 8 people in a vehicle the cost is $32. Assume the base charge is y. So

$y+8x = 32, y + 8(3) = 32.$

$y = 32 - 24 = 8.$

So the base charge per vehicle is $8.

Step 3:

The charges for a bus containing 30 people is calculated as such.

$y + 8x,$ where $y=8$ and $x = 30.$

$y + 8x = 8 + 30(3) = 98.$

So the cost of a bus containing 30 people is $98.