Question

Two mechanics worked on a car. The first mechanic charged $105 per hour, and the second mechanic charged $120 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $2175. How long did each mechanic work?

Answer 1

The first mechanic charged $105 per hour.

The second mechanic charged $120 per hour.

The mechanics worked for a combined total of 20 hours

Let the first mechanic work for x hours

Then

`\begin{gathered} 105x+(20-x)120\text{ =2175} \\ 105x+2400-120x=2175 \\ \text{collect like terms} \\ 105x-120x=2175-2400 \\ -15x=-225 \\ \\ \text{Divide both sides by -15} \\ \frac{\text{-15x}}{\text{-15}}=-\frac{225}{\text{-15}} \\ \\ x=15 \end{gathered}`

The first mechanic work for x hours which 15hours

The second mechanic work for (20-x ) hours which is 20-15=5hours

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