Equations and Problem Solving
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What You'll Learn
- To define a variable in terms of another variable
- To model distance-rate-time problems
… And Why
To solve real-world problems involving distance, rate, and time, as in Examples 3–5
Defining Variables
Some problems contain two or more unknown quantities. To solve such problems, first decide which unknown quantity the variable will represent. Then express the other unknown quantity or quantities in terms of that variable.
Problem Solving Hint
For Example 1, drawing a diagram will help you understand the problem.
Defining One Variable in Terms of Another
GeometryThe length of a rectangle is 6 in. more than its width. The perimeter of the rectangle is 24 in. What is the length of the rectangle?
Consecutive integers differ by 1. The integers 50 and 51 are consecutive integers, and so are – 10, – 9, and – 8. For consecutive integer problems, it may help to define a variable before describing the problem in words. Let a variable represent one of the unknown integers. Then define the other unknown integers in terms of the first one.
Consecutive Integer Problem
The sum of three consecutive integers is 147. Find the integers.
