Question

Two mechanics worked on a car. The first mechanic charged $65 per hour, and the second mechanic charged $95 per hour. Themechanics worked for a combined total of 35 hours, and together they charged a total of $2725. How long did each mechanic work?Х5?First mechanic: hoursSecond mechanic: hours

Answer 1

Given

Two mechanics worked on a car.

The first mechanic charged $65 per hour, and the second mechanic charged $95 per hour.

The mechanics worked for a combined total of 35 hours, and together they charged a total of $2725.

To find: How long did each mechanic work?

Step-by-step explanation:

It is given that,

The first mechanic charged $65 per hour, and the second mechanic charged $95 per hour.

Also,

The mechanics worked for a combined total of 35 hours, and together they charged a total of $2725.

Let x be the number of hours the first mechanic worked and y be the number of hours the second mchanic worked.

Then,

`\begin{gathered} x+y=35\text{ \_\_\_\_\_\_\_\lparen1\rparen} \\ 65x+95y=2725\text{ \_\_\_\_\_\_\_\_\lparen2\rparen} \end{gathered}`

From (1),

`x=35-y`

Therefore,

`\begin{gathered} 65(35-y)+95y=2725 \\ 2275-65y+95y=2725 \\ 30y=2725-2275 \\ 30y=450 \\ y=(450)/(30) \\ y=15 \end{gathered}`

Then,

`\begin{gathered} x=35-15 \\ x=20 \end{gathered}`

Hence, first mechanic worked 20 hours and second mechanic worked 15 hours.