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.

1 answer

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.