Question

Samuel's air conditioning unit stopped working. He has to find a repair company to fix the unit. He decides to compare the costs of two companies based on their service fees and labor costs.

Cool Ar Plus charges a $25 service fee for coming out to the house. They also charge $25 per hour of work that they perform
- Cool Breeze Ar charges a $40 service fee for coming out to the house. They also charge $15 per hour of work that they perform
The system of linear equations shown can be used to represent this situation. In the system of linear equations, h represents the amount time (in hours) It takes the company to perform the work and C
the total cost in dollars) of the air conditioning work performed by the company
25h + 25 = c
15h + 40 = C
- Determine the point in time, in hours, when the two companies cost the same amount of money.
- Identify the cost of the repairs, in dollars, when the two companies cost the same amount of money,
Show your work or explain how you determined your answers.
Enter your answers and your work or explanation in the box provided

Answer 1

(a) 1.5 hours

(b) They both charge $62.50

Explanation:

The given linear equations are:

`25h + 25 = c` ---- Cool Ar Plus

`15h + 40 = c` --- Cool Breeze Ar

Solving (a): The time they charge the same amount.

To do this, we equate both equations

`25h + 25 = 15h + 40`

Collect like terms

`25h - 15h = 40 - 25`

`10h = 15`

Divide both sides by 10

`h = 1.5`

This implies that they charge the same at 1.5 hour

Solving (b): The same amount they charge

To do this, we substitute 1.5 for h in any of the given equations

`25h + 25 = c`

`25 * 1.5 + 25 = c`

`62.5 = c`

`c=62.5`

This implies that they charge $62.50