Two mechanics worked on a car. the first mechanic worked for
10
hours, and the second mechanic worked for
15
hours. together they charged a total of
$2575
. what was the rate charged per hour by each mechanic if the sum of the two rates was
$210
per hour?

Create equations:
10X+15y=2575.
X+Y=210.
Solve for X: X=210-Y, and sub it into the other equation: 10(210-Y)+15Y=2575. Solve for Y: 2,100-10y+15y=2575, 5y=475, y=95.
Sub Y into the original problem: X+95=210. Solve: X=115.
The first mechanic charges $115 per hour and the second charges $95 :)

You can use 2 equations for this. let's use x to stand for 10 hour mechanic rate and y for 15 hour mechanic rate. So for first equation we know the total amount of money made was 2575. we also know that each mechanic charged 10x (10 hours times his pay rate) and 15y (15 hours times other payrate). So:
10x + 15y = 2575

we also know that the 2 rates added together equals 210. this means:
x + y = 210

we can actually solve for x or t on this second one easily:
x= 210 - y. Or y = 210 - x

I'm going to use the x= 210 - y but you could use the other one.

since I know what x equals I can actually substitute it in on the first equation like so:
10 * (210 - y) + 15y = 2575

notice how I combined the 2 equations
2100 - 10y + 15y = 2575

move the 2100 to other side by subtracting and combine y' s
5y = 475
y = 95

So so we know the 15 hour employee charged $95 an hour. we can plug this into second equation and find other wage. like this:
x = 210 - 95
x = 115

So this 1st guy made $115 an hour