Question

A) Find the linear equations that model the costs of a one-day rental where Jeff dives miles over the 100-mile limit with the national and local companies. B) Under what conditions would it be less expensive to rent from the national car rental company? Don’t forget that the first 100 miles are included in the daily fee.

Answer 1

Step 1

Find the system of equations from the data given for the national company and local company

Let x = miles after 100 miles, y=over all cost

`\begin{gathered} The\text{ standard equation of a line is y=mx+b} \\ For\text{ the system of equations, we will have;} \\ \end{gathered}`
`\begin{gathered} y_1=51+0.2x--(1) \\ y_2=35+0.3x--(2) \end{gathered}`

Step 2

Find the linear equations that model the costs of a one-day rental where Jeff dives miles over the 100-mile limit with the national and local companies.

For the national company; m miles over the hundred miles limit is driven, hence x=m

`y_1=51+0.2m`

For the local company; m miles over the hundred miles limit is driven, hence x=m

`y_2=35+0.3m`

Step 3

Under what conditions would it be less expensive to rent from the national car rental company? Don’t forget that the first 100 miles are included in the daily fee.

For this, we will equate both equations and solve for x