I am not sure how to solve this problem.

Utiltiy costs at Service, inc are a mixture of fixed and variable components. Records indicate that utiltiy costs are an average of $0.40 per hour at an activity level of 9,000 machine hours and $0.25 per hour at an activity level of 18,000 machine hours. Assuming that this actaivity is within the relevant range, what is the expecterd total utility cost if the company works 13,000 machine hours?

It's a simple two-variable equation.

Since operation occurs over the relevant range, fixed costs are equal in both cases. Also within the relevant range, the variable cost per unit is constant.

From this we can infer:

9,000x + y = 3600
18,000x + y = 4500

If you solve the first equation for y and put that into the second equation you can solve for x. Once you have x, you can put that back into either equation and compute the fixed costs (y).

y = 3,600 - 9,000x
18,000x + 3,600 - 9,000x = 4500
x = 0.10
y = 3,600 - 9,000(0.10)
y = 2,700

You can put x and y in both original equations and see that it works for both.

When you have that, you can easily see that the cost for running 13,000 hours is $4,000.