Question

Two companies provide service in a community.• The total cost of a service call for x hours of labor at company A is modeled byy = 28x+ 32.5.• The initial charge for a service call at company B is $3 less than at company A, but their hourly rate is 25% greater.What is the expected total cost of a service call for 6 hours of labor at company B?

Answer 1

The expected total cost of a service call for 6 hours of labor at company B is $239.5

Explanation:

To solve this, we'll find the expression that models the cost at company B.

First, we'll calculate the hourly rate. We know that is 25% greater than the $28 rate from company A, so we can use a rule of three as following:

This way,

`\begin{gathered} x=28*(125)/(100) \\ \\ \Rightarrow x=35 \end{gathered}`

Therefore, we'll have that the hourly rate for company B is $35.

Now, we know that the charge for service is $3 less than at company A. This way,

`32.5-3=29.5`

We can conclude that the charge for service at company B is $29.5

Using this data, we'll have that the expression that models the cost for company B is:

`y=35x+29.5`

Using x = 6 (six hours of labor),

`\begin{gathered} y=35(6)+29.5 \\ \\ \Rightarrow y=239.5 \end{gathered}`

Therefore, we can conclude that the expected total cost of a service call for 6 hours of labor at company B is $239.5