SOLUTION: Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for five hours. Together they charged a total of$1325. What was the rate charg

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Question 707469: Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for five hours. Together they charged a total of$1325. What was the rate charged per hour by each mechanic if the sum of the two rates was $100 per hour?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 1st mechanic's rate = +a+ dollars/hr
Let the 2nd mechanic's rate = +b+ dollars/hr
given:
(1) +20a+%2B+5b+=+1325+
(2) +a+%2B+b+=+100+
------------------
Multiply both sides of (2) by 5 and
subtract (2) from (1)
(1) +20a+%2B+5b+=+1325+
(2) +-5a+-+5b+=+-500+
+15a+=+825+
+a+=+55+
and, since
(2) +55+%2B+b+=+100+
(2) +b+=+45+
The 1st mechanic's rate was $55/hr
The 2nd mechanic's rate was $45/hr
check answers:
(1) +20%2A55+%2B+5%2A45+=+1325+
(1) +1100+%2B+225+=+1325+
(1) +1325+=+1325+
OK