Two mechanics worked on a car. the first mechanic charged $85 per hour, and the second mechanic charged $120 per hour. the mechanics worked for a combined total of 20 hours, and together they charged a total of $1875 . how long did each mechanic work?

Let's make a system of equations.
F=First mechanic
S=Second mechanic
F+S=20
85F+120S=1875
Let's make the first equation equal S.
S=20-F; We can plug this in as S in the second equation.
85F+120(20-F)=1875
85F+2400-120F=1875
Add like terms.
-35F+2400=1875
Subtract 2400.
-35F=-525
Divide.
-525÷-35=15=F
So, the first mechanic worked 15 hours and the second one had to work 5 since they worked 20 together. Let's check.
85(15)+120(5)
1,275+600
1,875
So, the first mechanic worked 15 hours and the second mechanic worked 5 hours.