SOLUTION: Two mechanics worked on a car. The first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1750 . What was the rate charg

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Two mechanics worked on a car. The first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1750 . What was the rate charg      Log On


   

Question 839002: Two mechanics worked on a car. The first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1750 . What was the rate charged per hour by each mechanic if the sum of the two rates was $160 per hour?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = amount charged by 1st mechanic
Let +b+ = amount charged by 2nd mechanic
Let +a%2F15+ = the rate for the 1st mechanic
Let +b%2F5+ = the rate for the 2nd mechanic
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(1) +a+%2B+b+=+1750+
(2) +a%2F15+%2B+b%2F5+=+160%2F1+ dollars/hr
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Multiply both sides of (2) by +15+
(2) +a+%2B+3b+=+2400+
Subtract (1) from (2)
(2) +a+%2B+3b+=+2400+
(1) +-a+-+b+=+-1750+
+2b+=+650+
+b+=+325+
and, since
(1) +a+%2B+b+=+1750+
(1) +a+=+1750+-+b+
(1) +a+=+1425+
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The 1st mechanic's rate is:
+1425%2F15+=+95+
$95/hr
The 2nd mechanic's rate is:
+325%2F5+=+65+
$65/hr
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check:
(1) +a+%2B+b+=+1750+
(1) +1425+%2B+325+=+1750+
(1) +1750+=+1750+
OK