Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second charged $45 per hour. The mechanics worked for a combined total of 35 hours, and together they charged $1775. How long did each mechanic work?

A worked 20 hours and B worked 15 hours.

Step-by-step explanation:

Given:

Mechanic A hourly rate = $55

Mechanic B hourly rate = $45

Total charged = $1775

Let's assume Mechanic A worked 'A' amount of hours and Mechanic B worked 'B' amount of hours, then

Step 1:

First equation: A + B = 35

Second equation: 55xA + 45xB = 1775

Step 2:

First equation can be written as: A = 35 - B

Step 3: Replace value of A in second equation

Second equation: 55x(35-B) + 45B = 1775

                            : 1925 - 55B + 45B = 1775

                            : (1925 - 1775 )/10 = B

                            : B = 15 hours

A worked = 35 - 15

                = 20 hours

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