91Ó°ÊÓ

Bob's Pest Removal Service specializes in removing wild creatures (skunks, bats, reptiles, etc.) from private homes. He charges \(\$ 70\) to go to a house plus \(\$ 20\) per hour for his services. Let \(y\) be the total amount (in dollars) paid by a household using Bob's services and \(x\) the number of hours Bob spends capturing and removing the animal(s). The equation for the relationship between \(x\) and \(y\) is $$ y=70+20 x $$ a. Bob spent 3 hours removing a coyote from under Alice's house. How much will he be paid? b. Suppose nine persons called Bob for assistance during a week. Strangely enough, each of these jobs required exactly 3 hours. Will each of these clients pay Bob the same amount, or do you expect each one to pay a different amount? Explain. c. Is the relationship between \(x\) and \(y\) exact or nonexact?

Step by step solution

01

Calculate the Payment for Alice's Case

Bob spent 3 hours at Alice's house, so we substitute \(x = 3\) into the equation \(y = 70 + 20x\). Thus, we calculate \(y = 70 + 20(3) = 70 + 60 = \$130\). Therefore, Alice will have to pay Bob \$130.

02

Answer Client Payment Question

Given that Bob spends exactly 3 hours at each of the nine jobs, each of these clients will pay him the same amount as Alice. This is since the variable \(x\) is the same for each job and the cost is determined by the fixed \$70 fee and the hourly rate.

03

Describe the Relationship

The relationship between \(x\) and \(y\) in the equation \(y = 70 + 20x\) is exact because for each hour \(x\) of service, there is a definite total amount \(y\) to be paid. There is no range or approximation, but a precise payment for each value of \(x\).

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