Two mechanics worked on a car. The first mechanic charged $45 per hour, and the second mechanic charged $75 per hour. The mechanics worked for a combined total of 15 hours, and together they charged a total of $825. How long did each mechanic work?

first mechanic worked for 10hours while the second mechanic worked for 5 hours.

Step-by-step explanation:

Let x be the number of hours first mechanic worked at $45 per hour

Let y be the number of hours second mechanic worked at $75 per hour

From the question, we know that the 2 mechanics did a combined work for 15hours and charged $825

Equation 1 is x + y= 15 where x is the number of hours the first mechanic worked, and y is the number of hours the second mechanic worked

45x+75y = 825

x+y =15; therefore y = 15-x

We will now replace y in equation 45x+75y = 825 with 15-x

Therefore,

45x+75(15-x)= 825

45x + 1125 - 75x = 825

45x - 75x = 825 - 1125

-30x = -300

Divide both sides by -30

x = -300/-30

x = 10

If x is 10 then y has to be 5 since combined work hours of both mechanics is 15 hours.

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