Question

Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $105 per hour. The mechanics worked for a combined total of 35 hours, and together they a total of $3475. How long did each mechanic work?

First mechanic: _ hours

Second mechanic: _ hours

Answer 1

First mechanic: 20 hours

Second mechanic: 15 hours

Explanation:

Let's use a system of equations to solve the problem.

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

We can set up two equations based on the given information:

x + y = 35 (equation 1)

95x + 105y = 3475 (equation 2)

We can solve equation 1 for one of the variables:

x = 35 - y

Substitute this expression for x into equation 2 and solve for y:

95(35 - y) + 105y = 3475

3325 - 95y + 105y = 3475

10y = 150

y = 15

So the second mechanic worked 15 hours. Substituting y = 15 into equation 1 gives:

x + 15 = 35

x = 20

Therefore, the first mechanic worked 20 hours.

Answer:

First mechanic: 20 hours

Second mechanic: 15 hours