SOLUTION: Two mechanics worked on a car. The first mechanic charged $105 per hour, and the second mechanic charged $50 per hour. The mechanics worked for a combined total of 20 hours, and to

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Two mechanics worked on a car. The first mechanic charged $105 per hour, and the second mechanic charged $50 per hour. The mechanics worked for a combined total of 20 hours, and to      Log On


   

Question 1184557: Two mechanics worked on a car. The first mechanic charged $105 per hour, and the second mechanic charged $50 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1825. How long did each mechanic work?
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


First a traditional algebraic setup for solving the problem....

x = hours at $105 per hour
20-x = hours at $50 per hour

Total charge for 20 hours was $1825:

105%28x%29%2B50%2820-x%29=1825

Solve using basic algebra.

And a solution method without algebra, using logical reasoning and some mental arithmetic....

All 20 hours at $105 per hour would cost $2100; all 20 hours at $50 per hour would cost $1000; the actual cost was $1825.

Look at the three costs on a number line -- 1000, 1825, and 2100 -- and observe/calculate that 1825 is 825/1100 = 3/4 of the way from 1000 to 2100.

That means 3/4 of the hours were at the higher rate.

ANSWER: 3/4 of 20 hours, or 15 hours, at $105 per hour; the other 5 hours at $50 per hour

CHECK: 15(105)+5(50)=1575+250=1825