Question

Solve each problem. The cost of renting a rototiller is $\$ 17.50$ for the first hour and $\$ 8.95$ for each additional hour. How long can a person have the rototiller if the cost must be less than $\$ 75 ?$ (FIGURE CANNOT COPY)

Name: Problem 90, Chapter 1: College Algebra
Uploaded: 2020-07-16T20:12:14-08:00
Duration: 1 min 25 s
Channel: Jeffrey Morris
Description: Solve each problem. The cost of renting a rototiller is 17.50 for the first hour and 8.95 for each additional hour. How long can a person have the rototiller if the cost must be less than 75 ? (FIGURE CANNOT COPY)

   Solve each problem.
The cost of renting a rototiller is $\$ 17.50$ for the first hour and $\$ 8.95$ for each additional hour. How long can a person have the rototiller if the cost must be less than $\$ 75 ?$
(FIGURE CANNOT COPY)

College Algebra

R. David Gustafson,… 11th Edition

Chapter 1, Problem 90

Instant Answer

Solved by Expert Jeffrey Morris

07/16/2020

Step 1

The cost of renting the rototiller is $17.50 for the first hour and $8.95 for each additional hour. We want to find out how long a person can have the rototiller if the cost must be less than $75. So, we can write the inequality as: \[17.50 + 8.95x < 75\] where Show more…

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Solve each problem. The cost of renting a rototiller is $\$ 17.50$ for the first hour and $\$ 8.95$ for each additional hour. How long can a person have the rototiller if the cost must be less than $\$ 75 ?$ (FIGURE CANNOT COPY)

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Key Concepts

Algebraic Modeling

This concept involves translating a real-world situation into an algebraic expression or equation. It includes identifying fixed costs, variable costs, and constructing a formula to represent the total cost based on the amount of time rented.

Linear Inequalities

This concept involves setting up and solving inequalities to determine the range of values that satisfy a given condition. In real-world problems, like cost restrictions, inequalities allow for determining maximum or minimum limits based on given constraints.

Piecewise Functions

Piecewise functions describe situations where different rules or formulas apply to different parts of the domain. In rental cost problems, the pricing may vary based on the duration (with an initial fee and then a recurring fee), making the cost function piecewise.

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