172 Chapter 3 Solving Equations Section 3.5 Applications and Problem Solving Key Concepts Problem-Solving Flowchart for Word Problems Step 1 Read the problem completely. Step 2 Assign labels to unknown quantities. Step 3 Write an equation in words. Step 4 Write a mathematical equation. Step 5 Solve the equation. Step 6 Interpret the results and write the final answer in words. Examples Example 1 Subtract 5 times a number from 14. The result is 6. Find the number. Step 1 Let n represent the unknown number. Step 2 Step 3 from 14 subtract 5n result is 6 e e e 14 Step 4 Step 5 5n 6 14 14 5n 6 14 5n 20 5n 5 20 5 n 4 The number is 4. Step 6 Example 2 An electrician needs to cut a 20-ft wire into two pieces so that one piece is four times as long as the other. How long should each piece be? Step 1 Let x be the length of the shorter piece. Step 2 Then 4x is the length of the longer piece. The two pieces added together will be 20 ft. Step 3 Step 4 Step 5 Step 6 x 4x 20 5x 20 5x 5 20 5 x 4 One piece of wire is 4 ft and the other is 4(4 ft), which is 16 ft. Section 3.1 For Exercises 1 and 2, list the coefficients of the terms. 1. 3a2 5a 12 2. 6xy y 2x 1 For Exercises 3–6, determine if the two terms are like terms or unlike terms. 3. 5t2, 5t 4. 4h, 2h 5. 21, 5 6. 8, 8k Chapter 3 Review Exercises
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