Need algebra help for solving a value mixture problem using a system of linear equations

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Two mechanics work on a car,  The 1st one worked 20 hrs, and the 2nd one for 15 hrs. Together they charged $2875.  What was the rate charged per hour by each mechanic if the sum of the two was $170 per hour?

Nov 14th, 2015

Thank you for the opportunity to help you with your question!

We need to assign variables here.  What do we not know?

We do not know the rate charged by the first mechanic.  Let us call it x.

We do not know the rate charged by the 2nd mechanic who worked 15 hours. call it y.

We see that 20*x + 15*y = 2875  because  rate * time = quantity of money.

we also see that  x + y = 170  the sum of their rates.

We solve this system by substitution:

y = 170 - x

20x + 15*(170 - x) = 2875

20x + 2550 - 15x = 2875

5x + 2550 = 2875

5x = 325


y = 170 - x = 170 - 65 = 105

Therefore the 1st mechanic who worked 20 hours charges $65 per hour

and the 2nd mechanic who worked 15 hours charges $105 per hour

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 14th, 2015

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