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 [tex]= \frac{20-14}{4-2} = \frac{6}{2} = 3.[/tex]
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
[tex]y+8x = 32, y + 8(3) = 32.[/tex]
[tex]y = 32 - 24 = 8.[/tex]
So the base charge per vehicle is $8.
Step 3:
The charges for a bus containing 30 people is calculated as such.
[tex]y + 8x,[/tex] where [tex]y=8[/tex] and [tex]x = 30.[/tex]
[tex]y + 8x = 8 + 30(3) = 98.[/tex]
So the cost of a bus containing 30 people is $98.