Question

Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $5 per hour. The mechanics worked for acombined total of 20 hours, and together they charged a total of $1850. How long did each mechanic work?First mechanic: hoursSecond mechanic: hours

Answer 1

We know that two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $85 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1850.

To find the answer we must represent the situation with a system of equations.

`\begin{gathered} A+B=20\ldots(1) \\ 115A+85B=1850\ldots(2) \end{gathered}`

Where,

A: Number of hours that the first mechanic worked

B: Number of hours that the second mechanic worked

First, we must multiply equation 1 by -115

`\begin{gathered} -115(A+B)=-115\cdot20 \\ -115A-115B=-2300\ldots(3) \end{gathered}`

Second, we must add equations 2 and 3

`\begin{gathered} 115A+85B=1850 \\ -115A-115B=-2300 \\ ---------------- \\ 0-30B=-450\ldots(4) \end{gathered}`

Now, we can solve equation 4 for B

`\begin{gathered} -30B=-450 \\ B=(-450)/(-30) \\ B=15 \end{gathered}`

Then, we must replace the value of B in the equation 1 and finally we must solve for A

`\begin{gathered} A+15=20 \\ A=20-15 \\ A=5 \end{gathered}`

Answer:

First mechanic: 5 hours

Second mechanic: 15 hours