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} cThus, the company that charges less for a 2-hour job is Mike's Repair which charges 200.

Therefore, the correct answer is Mike's Repair.

part (b):

To use my understanding of tables, graphs and equations to explain why I chose my answer in part (a):

The fixed charge of 125 by Sam's Repair accounted for his charges,

But Mike's Repair charges 0 as a fixed charge. Hence, the reduced charges especially when the number of hours for the job is less.

[tex]\begin{gathered} 75x+125\leq100x \\ 75x-100x\leq-125 \\ -25x\leq-125 \end{gathered}$$\begin{gathered} x\ge\frac{-125}{-25} \\ \\ x\ge5 \end{gathered}$

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