SOLUTION: Problem Page Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second mechanic charged $80 per hour. The mechanics worked for a combined total of 25 h

Algebra ->  Linear-equations -> SOLUTION: Problem Page Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second mechanic charged $80 per hour. The mechanics worked for a combined total of 25 h      Log On


   

Question 1110784: Problem Page Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second mechanic charged $80 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $1750 . How long did each mechanic work?
Found 3 solutions by josgarithmetic, TeachMath, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, time of first mechanic
y, time of second mechanic

system%28x%2By=25%2C55x%2B80y=1750%29
Simplify and solve the system.
system%28x%2By=25%2C11x%2B16y=350%29

system%2811x%2B11y=275%2C11x%2B16y=350%29

%2811x%2B16y%29-%2811x%2B11y%29=350-275
5y=75
highlight%28y=15%29--------the second mechanic
-
x%2By=25
x=25-y
x=25-15
highlight%28x=10%29---------the first mechanic

Answer by TeachMath(96) About Me  (Show Source):
You can put this solution on YOUR website!
wrong, wrong, wrong! it's impossible for times to be 20 and 25 hours.

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
55*x + 80*(25-x) = 1750

55x + 2000 - 80x = 1750

-25x = 1750-2000

-25x = -250   ====>  x = %28-250%29%2F%28-25%29 = 10.


Answer.  1-st mechanic worked 10 hours.

         2-nd mechanic worked 25-10 = 15 hours.


Check.  10*55 + 15*80 = 1750.    ! Correct !

Solved.

=====================

Be aware: The solution by @josgarithmetic and his answer   20 hours   and   25 hours   are   W R O N G.


    josgarithmetic, don't you think that it is JUST TIME for you to leave this forum FOREVER ? ? ?