Moving Day. Valley Truck Rentals charges 25.50 dollars per...

Name: Problem 95, Chapter 4: Intermediate Algebra
Uploaded: 2020-05-16T23:13:57-08:00
Duration: 1 min 8 s
Channel: Elizabeth Xu
Description: Moving Day. Valley Truck Rentals charges 25.50 dollars per day and 0.75 dollars per mile to rent a 14-foot truck. Nationwide Truck Rentals' daily charge for the same vehicle is 36.75 dollars and 0.60 dollars per mile. If the truck is rented for one day, for what range of miles driven is Nationwide's plan better?

Moving Day. Valley Truck Rentals charges 25.50 dollars per day and 0.75 dollars per mile to rent a 14-foot truck. Nationwide Truck Rentals' daily charge for the same vehicle is 36.75 dollars and 0.60 dollars per mile. If the truck is rented for one day, for what range of miles driven is Nationwide's plan better?

Key Concepts

Linear Functions

Linear functions are mathematical expressions that model relationships with a constant rate of change. They are often used to compare costs over time or usage, such as determining the total cost based on a fixed daily fee plus a variable cost per mile. In a cost comparison scenario, the constant daily charge is the y-intercept while the per-unit cost (per mile, for example) is the slope of the function.

Inequalities

Inequalities are mathematical expressions that show the relationship of values where one side is greater or less than the other. In the context of comparing two cost models, setting up an inequality helps determine under what conditions one pricing plan is more cost effective than the other by finding the range of values (such as miles driven) that satisfy the desired cost advantage.

Break-even Analysis

Break-even analysis involves finding the point at which two cost functions are equal, which is often called the break-even point. This concept is critical in decision-making because it identifies the threshold where the costs of two alternatives are identical, helping to determine which option is more economical beyond that point.

Cost Structure Comparison

Cost structure comparison examines the components that make up different pricing models, typically involving fixed costs (like a daily fee) and variable costs (like a per-mile rate). By understanding and comparing these components through mathematical modeling, one can select the option that minimizes total cost for a range of usage scenarios.

Transcript

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