Question

the cost to replace a water pump in a sports car was $969. this included $435 for the water pump and $89 per hour for labor. how many hours of labor were required to replace the water pump?
hr
the cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use over 900 min. for a month in which the executives cellular phone bill was $93.80, how many minutes did the executive use the phone?
min

Explanation:

Step1: Set up the equation for the labor - related problem

Let \(x\) be the number of hours of labor. The total cost \(C\) to replace the water pump is the sum of the cost of the pump and the cost of labor. The cost of the pump is \(435\) dollars and the cost of labor is \(89x\) dollars. So, \(C = 435+89x\). We know that \(C = 969\). Then the equation is \(969=435 + 89x\).

Step2: Solve the equation for \(x\)

Subtract \(435\) from both sides of the equation:

$$
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$$

Divide both sides by \(89\): \(x=\frac{534}{89}=6\).

Step3: Set up the equation for the phone - related problem

Let \(y\) be the number of minutes over \(900\) minutes. The monthly bill \(B\) is \(35+0.4y\). We know that \(B = 93.80\). So the equation is \(93.80=35 + 0.4y\).

Step4: Solve the equation for \(y\)

Subtract \(35\) from both sides:

$$
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$$

Divide both sides by \(0.4\): \(y=\frac{58.8}{0.4}=147\). The total number of minutes is \(900 + y=900+147 = 1047\).

Answer:

For the labor problem: \(6\) hr. For the phone problem: \(1047\) min.