Question

Sebastian hired a company to paint his apartment. The painting company charges afixed fee of $125.50 plus $22 per hour to paint an apartment.Part A: Write an equation that can be used to determine c, the total amount in dollarsthat the painting company charges to paint an apartment in h hours.Part B: The painting company charged a total of $455.50 to paint Sebastian'sapartment. How many hours did it take to paint Sebastian's apartment? Show orexplain how you got your answer.

Answer 1

`c=22h+125.50`

It took 15 hours to paint Sebastian's apartment

Explanation:

This situation can be represented by a linear function since it has a constant rate of change per hour, linear functions are represented by the following equation:

`\begin{gathered} c=mh+b \\ \text{where,} \\ m=\text{ constant rate of change} \\ b=\text{initial fee} \end{gathered}`

Part A. Therefore, the equation for the situation would be:

`c=22h+125.50`

Part B. If the total amount in dollars charged was $455.5, to determine the hours that it took, substitute c=455.50

`455.50=22h+125.50`

Solve for h.

`\begin{gathered} 22h=455.50-125.50 \\ 22h=330 \\ h=(330)/(22) \\ h=15 \end{gathered}`