Need assistance with word problem

Question

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 $2725

. What was the rate charged per hour by each mechanic if the sum of the two rates was $220

 per hour?

Answer 1

Let's let the variable x represent the rate of the first mechanic and the variable y represent the rate of the second mechanic. Then we can write the following equations based on the info in your problem:

x + y = $220

10x + 15y = $2725

Now we can use substitution to solve these two equations with two unknowns.

Using the first equation, we can write that x = 220 - y

Then we can substitute this expression for x int the second equation and solve for y:

10x + 15y = 2725

10(220 - y) + 15y = 2725

2200 - 10y + 15y = 2725

2200 + 5y = 2725

2200 + 5y - 2200 = 2725 - 2200

5y = 525

5y/5 = 525/5

y = $105 per hour for the second mechanic

The first mechanic's rate will be 220 -105 or $115 per hour