Question

Equation for Mechanic A: y = 160 + 35xEquation for Mechanic B: y = 100 + 55xWhich statement is true?A If her car repairs require less than 3 hours of labor, she should go to Mechanic A to get the lower repair cost.B If her car repairs require less than 3 hours of labor, she should go to Mechanic B to get the lower repair cost.C If her car repairs require exactly 3 hours of labor, she should go to Mechanic B to get the lower repair cost.D If her car repairs require exactly 3 hours of labor, she should go to Mechanic A to get the lower repair cost.

Answer 1

Let's test each scenario.

Scenario I

We are given both equations. We know that in this case, x is equivalent 0, 1, or 2 since it must be less than 3 hours. Let's test each possibility.

x = 0

`\begin{gathered} y=160+35(0) \\ y=160+0_{} \\ y=160 \end{gathered}`
`\begin{gathered} y=100+55x \\ y=100+55(0)_{} \\ y=100 \end{gathered}`

x = 1

`\begin{gathered} y=160+35(1) \\ y=160+35 \\ y=195 \end{gathered}`
`\begin{gathered} y=100+55(1) \\ y=100+55 \\ y=155 \end{gathered}`

With this information, we can immediately assume that no matter what, the first equation will always yield a larger sum than the second equation. In that case, Mechanic A is not favorable until Mechanic B's price equals that of Mechanic A.

We can visualize the graph to see that at 3 hours, however, the mechanic's will both charge the same price:

`\begin{gathered} y=160+35(3) \\ y=160+105 \\ y=265 \end{gathered}`
`\begin{gathered} y=100+55(3) \\ y=100+165 \\ y=265 \end{gathered}`Solution

• Mechanic A is always more expensive ,until it reaches 3 hours,. Therefore, answer choice A cannot be considered since the lower repair cost would come from Mechanic B.

,

• If the repair requires less than 3 hours, Mechanic B is always favored as a cheaper price. Therefore, this choice, ,Choice B,, is correct.

,

• When 3 hours of repair are required, we cannot consider Choice C because the