150 Chapter 2 Linear Equations and Inequalities Solving an Application Involving Consecutive Integers Example 4 The sum of two consecutive odd integers is 188. Find the integers. Solution: In this example we have two unknown integers. We can let x represent either of the unknowns. Step 1: Read the problem. Suppose x represents the first odd integer. Step 2: Label the unknowns. Then represents the second odd integer. Step 3: Write a verbal model. Step 4: Write a mathematical equation. Step 5: Solve for x. 1x 22 First a b second integer ab 1total2 integer x 1x 22 188 x 1x 22 188 2x 2 188 2x 2 2 188 2 2x 190 2x 2 190 2 x 95 The first integer is Step 6: Interpret the results and write the answer in words. x 95. The second integer is x 2 95 2 93. The two integers are and 95 93. Solving an Application Involving Consecutive Integers Example 5 Ten times the smallest of three consecutive integers is twenty-two more than three times the sum of the integers. Find the integers. Solution: Step 1: Read the problem. Let x represent the first integer. Step 2: Label the unknowns. represents the second consecutive integer. x 1 x 2 represents the third consecutive integer. Skill Practice 4. The sum of two consecutive even integers is 66. Find the integers. Classroom Example: p. 154, Exercise 22 TIP: With word problems, it is advisable to check that the answer is reasonable. The numbers and 95 are consecutive odd 93 integers. Furthermore, their sum is 188 as desired. Skill Practice 5. Five times the smallest of three consecutive integers is 17 less than twice the sum of the integers. Find the integers. Classroom Example: p. 154, Exercise 30 Answers 4. The integers are 32 and 34. 5. The integers are 11, 12, and 13.
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