Two mechanics worked on a car. the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800. what was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour ?

This can be solved by setting up a systems of equations. Let x be the hourly rate for the first mechanic and y be the hourly rate of the second.

Total money earned:
[tex]10x + 15y = 1800[/tex]
Sum of hourly rates:
[tex]x + y = 155[/tex]
To solve this, you solve for one equation first, substitute it in the second, then input it back into the first equation. I will first be solving for x.

[tex]x + y = 155 \\ x = 155 - y[/tex]
Input this into the other equation to find y:
[tex]10(155 - y) + 15y = 1800 \\ 1550 - 10y + 15y = 1800 \\ 5y = 250 \\ y = 50[/tex]
Input y into the first equation:
[tex]x + 50 = 155 \\ x = 105[/tex]

The first mechanic charges $105 per hour and the second mechanic charges $50 per hour.