Question

Truck Rentals A truck rental company rents a truck for one day by charging $\$ 31.95$ plus $\$ 0.89$ per mile. (a) Write a linear model that relates the cost $C,$ in dollars, of renting the truck to the number $x$ of miles driven. (b) What is the cost of renting the truck if the truck is driven 110 miles? 230 miles?

Name: Problem 49, Chapter 4: Algebra and Trigonometry
Uploaded: 2020-07-05T01:19:53-08:00
Duration: 1 min 24 s
Channel: Tiffany Tran
Description: Truck Rentals A truck rental company rents a truck for one day by charging 31.95 plus 0.89 per mile. (a) Write a linear model that relates the cost C, in dollars, of renting the truck to the number x of miles driven. (b) What is the cost of renting the truck if the truck is driven 110 miles? 230 miles?

   Truck Rentals A truck rental company rents a truck for one day by charging $\$ 31.95$ plus $\$ 0.89$ per mile.
(a) Write a linear model that relates the cost $C,$ in dollars, of renting the truck to the number $x$ of miles driven.
(b) What is the cost of renting the truck if the truck is driven 110 miles? 230 miles?

Algebra and Trigonometry

Michael Sullivan 10th Edition

Chapter 4, Problem 49

Instant Answer

Solved by Expert Tiffany Tran

07/05/2020

Step 1

95$ for one day and an additional $\$0.89$ per mile driven. This can be represented as a linear model where the cost $C$ is a function of the number of miles $x$ driven. The fixed price is the y-intercept and the cost per mile is the slope of the line. Therefore, Show more…

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Truck Rentals A truck rental company rents a truck for one day by charging $\$ 31.95$ plus $\$ 0.89$ per mile. (a) Write a linear model that relates the cost $C,$ in dollars, of renting the truck to the number $x$ of miles driven. (b) What is the cost of renting the truck if the truck is driven 110 miles? 230 miles?

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Key Concepts

Linear Model

A linear model represents a mathematical relationship where the change in one quantity is directly proportional to the change in another. In the context of cost calculations, it is often expressed as a constant base fee plus a variable cost that increases at a constant rate per unit of usage.

Slope-Intercept Form

This form of expressing a linear equation is written as y = mx + b, where 'm' represents the slope (the constant rate of change) and 'b' is the y-intercept (the initial value when x is zero). It is used to clearly identify the base cost and the additional cost per unit in cost models.

Substitution in Linear Equations

Substitution is the process of replacing the variable in an equation with a specific value to calculate the corresponding outcome. This technique is essential in cost modeling to determine the final cost for a given quantity of usage.

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