Question

Two mechanics worked on a car. The first mechanic charged $75 per hour, and the second mechanic charged $55 per hour. The mechanics worked for a

combined total of 25 hours, and together they charged a total of $1575. How long did each mechanic work?

Answer 1

10 and 15 hours

Explanation:

x+y =25 where x is the number of hours the first mechanic worked. y is the number of hours the second mechanic worked

75x+55y=1575

x+y =25 therefore y=25-x

We replace y in equation 75x+55y=1575 with 25-x

75x+55(25-x)=1575

now we solve for x

distribute 55 through the parentheses

75x+1375-55x=1575

combine like terms

20x+1375=1575

move the constant to the right-hand side and change its sign

20x=1575-1375

20x=200

divide each side by 20

x=10

If x is 10 then y has to be 15 since both worked a total of 25 hours.