SOLUTION: The "Build-it" Company hires out painters at p dollars per day and carpenters at c dollars per day. One job takes a carpenter 6 days and a painter 2 days to complete. The total cha

Question 12590: The "Build-it" Company hires out painters at p dollars per day and carpenters at c dollars per day. One job takes a carpenter 6 days and a painter 2 days to complete. The total charge is $970. A second job takes a carpenter 3 days and a painter 4 days to finish. The total charge is $770. A) write equations and solve them to find the cost of a days hire for a carpenter and a painter.
Answer by AdolphousC(70) (Show Source): You can put this solution on YOUR website!
This problem isn't really a Rate-of-Work Problem, it is actually a system of linear equations.

First Define your Variables, Let C be the Cost/Day for a Carpenter, and P be the Cost/Day for a Painter

Equation 1: 6c + 2p = 970

Equation 2: 3c + 4p = 770

Now you can solve this by grpahing, substitution or elimination, but for this answer, I will solve by elimination.

Choose one of your variables to get to be the same, I am going to choose C, so I need to multiply the Bottom equation by 2

6c + 2p = 970

2( 3c + 4p = 770 )

Now I get

6c + 2p = 970
6c + 8p = 1540

Subtract your two equations and you get -6p = -570, divide by -6 and P = 95.

That is, it cost $95.00/Day to hire a painter.

Now substitute P = 95 into one of your original equations

6c + 2(95) = 970

Simplfy 6c + 190 = 970
Subtract 190 from both sides 6c = 780
Dive by 6 on both sices c = 130

So it costs 130/day for a carpenter and 95/day for a painter.

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