Section 1.2 Applications of Linear Equations in One Variable 59 Answer 2. The integers are 21, 22, and 23. Solving a Linear Equation Involving Consecutive Integers Three times the sum of two consecutive odd integers is 516. Find the integers. Solution: Step 1: Read the problem carefully. Step 2: Label the unknown: Let x represent the first odd integer. Then x 2 represents the next odd integer. Step 3: Write an equation in words. 3(first odd integer) (second odd integer) 516 Step 4: Write a mathematical equation. Step 5: Solve for x. 3 3x 1x 22 4 516 312x 22 516 6x 6 516 6x 510 x 85 Example 2 Step 6: Interpret your results. The first odd integer is x: 85 The second odd integer is x 2: 85 2 87 Answer: The integers are 85 and 87. Skill Practice 2. Four times the sum of three consecutive integers is 264. Find the integers. 3. Applications Involving Percents and Rates In many real-world applications, percents are used to represent rates. • The sales tax rate for a certain county is 6%. • An ice cream machine is discounted 20%. • A real estate sales broker receives a % commission on sales. • A savings account earns 7% simple interest. 12 The following models are used to compute sales tax, commission, and simple interest. In each case the value is found by multiplying the base by the percentage. Sales tax (cost of merchandise)(tax rate) Commission (dollars in sales)(commission rate) Simple interest (principal)(annual interest rate)(time in years) I Prt 4 Avoiding Mistakes After completing a word problem, it is always a good idea to check that the answer is reasonable. Notice that 85 and 87 are consecutive odd integers, and three times their sum is 3(85 87), which equals 516.
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