Notice the following pattern
[tex]\begin{gathered} 259-187=72 \\ 331-187=144=2\cdot72 \end{gathered}[/tex]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
[tex]\begin{gathered} (1,187),(2,259) \\ \Rightarrow y-187=\frac{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}[/tex]Set h=x and c=y; thus, the answer to part A is
[tex]c=72h+115[/tex]Set h=6 and solve for c, as shown below.
[tex]\begin{gathered} h=6 \\ \Rightarrow c=72\cdot6+115=547 \end{gathered}[/tex]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
[tex]c=60h+195[/tex]Setting h=6 and solving for c,
[tex]\begin{gathered} h=6 \\ \Rightarrow c=60\cdot6+195=360+195=555 \\ \Rightarrow c=555 \end{gathered}[/tex]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.
