SOLUTION: Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2075. What was the rate charged

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Question 540994: Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2075. What was the rate charged per hour by each mechanic if the sum of the two rates was $190 per hour?
Answer by jpg7n16(66) (Show Source):
You can put this solution on YOUR website!
Let's start with what we know: mechanic X worked 20 hours (charging his rate) and mechanic Y worked 5 (charging his different rate). Together they made $2,075. How do you put that in an equation?

Part 2: the problem says that if you add mechanic X's and Y's charges together, it works out to $190/hour. How do you put that in an equation?

Now you have your two equations that you can "stack" and begin solving. To do that, you have to make each formula have either the same number of X's OR the same number of Y's. Then subtract them. I like to think of it as eliminating either X or Y from the other equation. So let's stack our 2 formulas:
1)
2)
We need to make equation 2 have either 20x or 5y. And I think it'd be much easier to make equation 2 have 5y, so multiply equation 2 by 5.
1)
2)
Now subtract one from the other. You're left with:

Now we know that mechanic X changes $75/hour for his work. So how much does mechanic Y charge? Just plug $75 into the easier equation and solve for Y.

Remember, when plugging back in to always choose the easier equation. You'll get the same answer no matter which one you choose, but why work that hard? Example:

See. Same answer, just more work.