SOLUTION: Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2225. What was the rate charg

Let x be the hourly rate of the first mechanic in dollars per hour, and
let y be the hourly rate of the second mechanic. 

Then from the condition, you have this system of two linear equations

20x + 15y = 2225,    (1)  
  x +   y =  130.    (2)


From equation (2), express y = 130 - x and substitute it into equation (1), replacing y. 
You will get a single equation for only one unknown

20x + 15*(130-x) = 2225  dollars.     (3)


Simplify and solve for x:

20x + 1950 - 15x = 2225  ====>

5x = 2225 - 1950 = 275  ====>  x =  = 55.


Thus the first mechanic's rate is $55 per hour.


Then the second mechanic's rate is $130 - $55 = $75 per hour.

Let x be the rate of the first mechanic in dollars per hour.
Then the rate of the second mechanic is (130-x) dollars per hour.

The "amount" equation is

20x + 15*(130-x) = 2225  dollars.


It is the same equation (3) of the PREVIOUS solution, and it leads to the same answer.