Solving a value mixture problem using a system of linear...
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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 $\mathrm{\$}1875$. What was the rate charged per hour by each mechanic if the sum of the two rates was $\mathrm{\$}110$ per hour?
First mechanic: $s◻$ per hour
Second mechanic: $s◻$ per hour
Explanation
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Step 1 ：Let's denote the rate of the first mechanic as x and the rate of the second mechanic as y. Then we have two equations: $20x+15y=1875$ and $x+y=110$.

Step 2 ：We can solve this system of equations to find the values of x and y.

Step 3 ：The solution to the system of equations gives the rates for the two mechanics. The first mechanic charges $45perhourandthesecondmechaniccharges$65 per hour.

Step 4 ：This makes sense as the sum of the two rates is $110perhourasgivenintheproblem.Also,whentheseratesaremultipliedwiththerespectivehoursworkedandadded,theygivethetotalchargeof$1875.

Step 5 ：Final Answer: The first mechanic charges $\boxed{{\displaystyle 45}}$ dollars per hour and the second mechanic charges $\boxed{{\displaystyle 65}}$ dollars per hour.