Chapter 8.8, Problem 48IP

To determine

Find the number of hours the mechanic is planning to work on the car.

Answer to Problem 48IP

At least 3 hours and forty five minutes.

Explanation of Solution

Given:

Cole is having his car repaired. The mechanic said it would cost at least $375 for parts and labour. If the cost of the parts was $150 and the mechanic charges $60 an hour, how many hours is the mechanic planning to work on the car?

Concept Used:

Let h be representing the number of hours the mechanic spent on the car.

The required inequality: $150+60h\ge 375$

Calculation:

The required inequality: $150+60h\ge 375$

  $\begin{array}{l}150+60h\ge 375\\ 150-150+60h\ge 375-150\text{[}\text{Subtract}150\text{from}\text{both}\text{sides}\text{]}\\ 60h\ge 225\\ \frac{60h}{60}\ge \frac{225}{60}\text{[}\text{Divide}\text{both}\text{sides}\text{by}60\text{]}\\ h\ge 3.75\text{hours}\\ h\ge 3\text{hours}\text{and}\text{45}\text{minutes}\end{array}$

Thus, the mechanic spent on the car is at least 3 hours 45 minutes.