Solve using the five "Steps for Solving Applied Problems."...

Solve using the five "Steps for Solving Applied Problems." Ciu Ling rented a cargo van to move her son to college. The rental company charges $\$ 42.00$ per day plus $\$ 0.32$ per mile. She used the van for 2 days, and her bill came to $\$ 158.88 .$ How many miles did she drive the van?

Solve using the five "Steps for Solving Applied Problems."
Ciu Ling rented a cargo van to move her son to college. The rental company charges $\$ 42.00$ per day plus $\$ 0.32$ per mile. She used the van for 2 days, and her bill came to $\$ 158.88 .$ How many miles did she drive the van?

Key Concepts

Unit Rates

Unit rates express the cost per single unit of measure, such as dollars per day or per mile. They are essential for translating the problem's descriptions into mathematical expressions by allowing you to multiply the unit rate by the number of units to obtain a subtotal, which, when combined with other components, yields the overall cost.

Applied Problem Solving Process

This concept involves following a structured series of steps to solve a problem, typically including understanding the problem, devising a plan, carrying out the plan, and reviewing the solution. In applied mathematics, these steps help break down real-world scenarios into manageable parts, ensuring that every component of the problem is addressed logically and systematically.

Linear Equations

A linear equation represents a relationship where one variable is directly proportional to another, often expressed in the form ax + b = c. In applied problems, setting up a linear equation allows for modeling relationships such as costs that have both fixed and variable components, making it possible to solve for an unknown quantity.

Fixed and Variable Costs

This concept distinguishes between costs that remain constant regardless of usage (fixed costs) and costs that change with the amount used (variable costs). In many real-life scenarios like rental services, understanding and separating these costs is key to formulating an equation that accurately represents the total cost.

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