Question

The cost of a car service is partly constant and partly varies with the time it takes to do the work .if cost 3500 naria for a 5 1/2 hour service and 2900 naira for a 4 hour service. Find the formula connecting cost , naira C with time ,T hours, hence find the cost of a 7 1/2 hour service.

Answer 1

Let the constant cost be C0 and the variable cost per hour be C1. We can use the information given to form two equations and solve for C0 and C1:

From the first service: 3500 = C0 + 5.5C1
From the second service: 2900 = C0 + 4C1

Subtracting the second equation from the first gives:
600 = 1.5C1
C1 = 400

Substituting back into either equation gives:
C0 = 1300

Therefore, the formula for cost, C, in terms of time, T, is:
C = 1300 + 400T

To find the cost of a 7 1/2 hour service, we simply substitute T = 7.5 into the formula:
C = 1300 + 400(7.5) = 4300 naira

Therefore, the cost of a 7 1/2 hour service is 4300 naira.