An electrician, carpenter, and a plumber are hired to work on a house. They are paid the following: elec. $20.00 per hour, carpenter $25.00 per hour, and the plumber $30.00 per hour. They worked a total of 23.25 hrs and earned a total of 571.25. If the electrician worked 4.75 hours more than the carpenter, how many hours did the plumber work?
what is asked in the problem?
How many hours did the plumber work?
Given:
They work a total of 23.25 hours and earned 571.25
Electrician 20.00/hr
Carpenter 25.00/hr
Plumber 30.00/hr
electrician work 4.75 hours more than the carpenter
Representation:
Let x = number of hrs the carpenter work
x + 4.75 = the number of hrs the electrician work
23.25 - (x + x + 4.75) = the number of hrs the plumer works.
23.25 - 2x - 4.75 or 18.5 - 2x
Equation:
20(x + 4.75) + 25 (x) + 30 (18.5 - 2x) = 571.25
20x + 95 + 25x + 555 - 60x = 571.25
-15x + 650 = 571.25
650 - 571.25 = 15x
78.75 = 15x
5.25 = x --------> number of hrs the carpenter works
x + 4.75 = number of hrs the electrician works
5.25 + 4.75 = 10hrs -------------> number of hrs the electrician works
23.25 - (10 + 5.25) = the number of hrs the plumber works
23.25 - 15.25 = 8 hrs -----------The number of hrs the plumber works
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