Section 1.2 Applications of Linear Equations in One Variable 57 Applications of Linear Equations in One Variable Section 1.2 1. Introduction to Problem Solving One of the important uses of algebra is to develop mathematical models for understanding Concepts 1. Introduction to Problem Solving 2. Applications Involving Consecutive Integers 3. Applications Involving Percents and Rates 4. Applications Involving Principal and Interest 5. Applications Involving Mixtures 6. Applications Involving Distance, Rate, and Time real-world phenomena. To solve an application problem, relevant information must be extracted from the wording of a problem and then translated into mathematical symbols.This is a skill that requires practice.The key is to stick with it and not to get discouraged. Problem-Solving Flowchart for Word Problems • Familiarize yourself with the problem. Estimate the answer, if possible. Step 1 Read the problem carefully. • Identify the unknown quantity or quantities. Let x represent one of the unknowns. Draw a picture and write down relevant formulas. Step 2 Assign labels to unknown quantities. Step 3 Write a verbal model. • Write an equation in words. • Replace the verbal model with a mathematical equation using x or another variable. Step 4 Write a mathematical equation. • Solve for the variable, using the steps for solving linear equations. Step 5 Solve the equation. • Once you’ve obtained a numerical value for the variable, recall what it represents in the context of the problem. Can this value be used to determine other unknowns in the problem? Write an answer to the word problem in words. Interpret the results and write the final answer in words. Step 6 Avoiding Mistakes Once you have reached a solution to a word problem, verify that it is reasonable in the context of the problem. To write an English statement as an algebraic expression, review the list of key terms given in Table 1-1. ab Addition: a b Subtraction: a b • the sum of a and b • the difference of a and b • a plus b • a minus b • b added to a • b subtracted from a • b more than a • a decreased by b • a increased by b • b less than a • the total of a and b Multiplication: Division: a b, • the product of a and b • the quotient of a and b • a times b • a divided by b • a multiplied by b • b divided into a • the ratio of a and b • a over b • a per b a b Table 1-1
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