Question

Ms. Lewis is hiring a carpenter to repair her shes. The cost of Carpenter L is shown in the table.

Answer 1

Notice the following pattern

`\begin{gathered} 259-187=72 \\ 331-187=144=2\cdot72 \end{gathered}`

This reflects a linear behavior; therefore, we can find the equation of the function represented by the table using two points on it and the equation below

`\begin{gathered} (1,187),(2,259) \\ \Rightarrow y-187=(259-187)/(2-1)(x-1) \\ \Rightarrow y-187=72(x-1)=72x-72 \\ \Rightarrow y=72x-72+187=72x+115 \\ \Rightarrow y=72x+115 \end{gathered}`

Set h=x and c=y; thus, the answer to part A is

`c=72h+115`

Set h=6 and solve for c, as shown below.

`\begin{gathered} h=6 \\ \Rightarrow c=72\cdot6+115=547 \end{gathered}`

The answers to part A are c=72h+115, and the cost of 6 hours of work is $547

Part B)

According to the problem, if c is the total cost and h is the number of hours; the equation that represents the function is

`c=60h+195`

Setting h=6 and solving for c,

`\begin{gathered} h=6 \\ \Rightarrow c=60\cdot6+195=360+195=555 \\ \Rightarrow c=555 \end{gathered}`

The answers to part B are c=60h+195, and the cost for 6 hours of work is $555.

Part C)

As we found in parts A and B, the least expensive carpenter for 6 hours of work is Carpenter L; however, this is the case if only 6 hours of work are required; if that changes, it could alter the answer.