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 $\$ 1875$. What was the rate charged per hour by each mechanic if the sum of the two rates was $\$ 110$ per hour?
First mechanic: $s \square$ per hour
Second mechanic: $s \square$ 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 $45 per hour and the second mechanic charges $65 per hour.

Step 4 ：This makes sense as the sum of the two rates is $110 per hour as given in the problem. Also, when these rates are multiplied with the respective hours worked and added, they give the total charge of $1875.

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