Chapter 1, Problem 14CT

(a)

To determine

To justify: the number of hours the total costs will be same

Answer to Problem 14CT

The total costs will be same for $2.1\text{ hours}$

Explanation of Solution

Given:

	Cost of parts	Labor cost per hour
Dealership	$24	$99
Local mechanic	$45	$89

Calculation:

Find when the costs are equal:

Define a variable.

  $Letx=Hours$

Write an equation.

  $99x+24=89x+45$

Subtract $89x$ from both sides.

  $10x+24=45$

Subtract 24 from both sides.

  $10x=21$

Divide both sides by 10.

  $x=2.1$

Conclusion:

The total costs will be same for $2.1\text{ hours}$

(b)

To determine

To find: where will the cost be cheaper.

Answer to Problem 14CT

When the number of hours is more than 2.1, it is cheaper at the local mechanic.

Explanation of Solution

Calculation:

When the number of hours is more than 2.1, it is cheaper at the local mechanic. When the number of hours is less than 2.1, it is cheaper at the dealership.

Conclusion:

When the number of hours is more than 2.1, it is cheaper at the local mechanic.