Please help me with this!

Two mechanics worked on a car. The first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1950. What was the rate charged per hour by each mechanic if the sum of the two rates was $200 per hour?

Question

Please help me with this!

Two mechanics worked on a car. The first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1950. What was the rate charged per hour by each mechanic if the sum of the two rates was $200 per hour?

mathstudent55 · Answer

Let's call the rates x and y.
If the sum of the rates is $200, can you write an equation using x and y to represent that fact?

ikou · Answer

Well I know that there can be two equations
the Value eq:  5x+15y+1950
and the Rate eq: x+y=200

mathstudent55 · Answer

Yes. I was asking for the rate equation only, but you have both equations already, and they are correct.
Now you need to solve the system of equations.

ikou · Answer

I don't really know how though

mathstudent55 · Answer

Ok. I'll explain it to you.
One method of solving a system of equation is called "the substitution method."
Let's use that method here.

mathstudent55 · Answer

The first step is to solve one equation for one variable.
We see that is easier to do that with the rate equation.
Can you solve the rate equation, x + y = 200, for x?

ikou · Answer

what happens to the y, and do I plug in 5x where the x should be

ikou · Answer

so if I plug in 5x to the equation and just ignore the y then I'd get 50, so x earns 50 an hour

mathstudent55 · Answer

First just solve x + y = 200 for x.
What do you get?

mathstudent55 · Answer

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