An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. Which of the following is a correct cost?

A. C (t) = 145 for 5 < x ≤ 6

B. C (t) = 145 for 6 < x ≤ 7

C. C (t) = 170 for 5 < x ≤ 6

D. C (t) = 170 for 6 < x ≤ 7

The total cost is given by the equation:

C (t) = 45 + 25 (h-1) where h is the number of hours worked.

We can check for each option in turn:

Option A:

Inequality 5 < x ≤ 6 means the hour is between 5 hours (not inclusive) to 6 hours (inclusive)

Let's take the number of hours = 5

C (5) = 45 + (5-1) * 25 = 145

Let's take the number of hours = 6

Then substitute into C (6) = 45 + (6-1) * 25 = 170

We can't take 145 because the value '5' was not inclusive.

Option B:

The inequality is 6 < x ≤ 7

We take number of hours = 6

C (6) = 25 (6-1) + 45 = 170

We take number of hours = 7

Then C (7) = 25 (7-1) + 45 = 195

Option C:

The inequality is 5 < x ≤ 6

Take the number of hours = 5

C (5) = 25 (5-1) + 45 = 145

Take the number of hours = 6

C (6) = 25 (6-1) + 45 = 170

We can't take the value 145 as '5' was not inclusive in the range, but we can take 170

Option D:

6 < x ≤ 7

25 (6-1) + 45 < C (t) ≤ 25 (7-1) + 45

170 < C (t) ≤ 195

Correct answer: C