Question

(Mike's Repair charges customers $100 perhour to fix your car. Sam's Repair chargesaccording to the equation y = 75x + 125where x = time in hours and y = cost indollars.a) Which company charges less for a 2-hour job?b) Use your understanding of tables,graphs, and equations to explain whyyou chose the company that you chose in part a)

Answer 1

The Solution:

For Mike's Repair charges, the equation:

`\begin{gathered} c=100x \\ \text{ where} \\ c=\text{ cost in dollars} \\ x=\text{ number of hours (time in hours)} \end{gathered}`

For Sam's Repair charges, the equation is given as:

`\begin{gathered} y=75x+125 \\ \text{ Where} \\ x=\text{time in hours} \\ y=\text{ cost in dollars} \end{gathered}`

Part (a):

Comparing the total charges for a 2-hour job, we have

`\begin{gathered} \text{ Mike's charges:} \\ \text{when x=2} \\ c=100x=100(2)=\text{ \$200} \end{gathered}`
`\begin{gathered} \text{ Sam's charges:} \\ \text{ When x=2} \\ y=75x+125=75(2)+125=150+125=\text{ \$275} \end{gathered}`

Clearly, we have that:

`\begin{gathered} x\ge(-125)/(-25) \\ \\ x\ge5 \end{gathered}`

So, the charges for both Repairs can only be equal if the number of hours is 5.