Two mechanics worked on a car. the first charged $115 per hour and the second charged $80 per hour. the mechanics worked for a combined total of 20 hours and together they charged a total of $1775. how long did each mechanic work ?

Total cost is 3,900. 115 x 20 = 2,300.
80 x 20 = 1,600. 2,300 + 1,600 = 3,900.

X= # hours first mechanic worked
y= # hours second mechanic worked

QUANTITY EQUATION
x + y= 20 hours

COST EQUATION
$115x + $80y= $1775

STEP 1:
multiply both sides of cost equation by -115

-115(x + y)= -115(20)
-115x - 115y= -2300

STEP 2:
add quantity equation and equation from step 1 together to solve for y

115x + 80y= 1775
-115x - 115y= -2300
x will cancel out

-35y= -525
divide both sides by -35
y= 15 hours second mechanic worked

STEP 3:
substitute y value in quantity equation to solve for x

x + y= 20
x + 15= 20
subtract 15 from both sides
x= 5 hours first mechanic worked

ANSWER: The first mechanic worked 5 hours and the second mechanic worked 15 hours.

Hope this helps! :)