Solving a value mixture problem using a system of linear equations

Question

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charge a total of $2800. What was the rate charged per hour by each mechanic if the sum of the two rates was $225 per hour?

Answer 1

Let the rate of the first mechanic be r₁ dollars per hour and the rate of the second mechanic be r₂ dollars per hour.

The total cost of the two mechanics is 10r₁+15r₂=$2800.

Also r₁+r₂=$225, so r₂=225-r₁ which can be substituted into the other equation:

10r₁+15(225-r₁)=2800,

10r₁+3375-15r₁=2800,

3375-2800=5r₁,

r₁=575/5=$115 per hour, so r₂=225-115=$110 per hour.

So the hourly rates are $115 and $110.