2 Solve Problems Involving Consecutive Integers In Chapter 2 we solved problems involving consecutive integers. Some applications involving consecutive integers lead to quadratic equations. EXAMPLE 2 Solve. Twice the sum of three consecutive odd integers is 9 less than the product of the smaller two. Find the integers. Solution Step 1: Read the problem carefully, and identify what we are being asked to fi nd. We must fi nd three consecutive odd integers. Step 2: Choose a variable to represent an unknown, and defi ne the other unknowns in terms of this variable. x the first odd integer x 2 the second odd integer x 4 the third odd integer Step 3: Translate the information that appears in English into an algebraic equation. Read the problem slowly and carefully, breaking it into small parts. is 9 less than Twice the sum of three consecutive odd integers Statement: ⎫⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎭ T Equation: 2x (x 2) (x 4) x(x 2) 9 Step 4: Solve the equation. " " the product of the smaller two. 2x (x 2) (x 4) x(x 2) 9 2(3x 6) x2 2x 9 Combine like terms; distribute. 6x 12 x2 2x 9 Distribute. 0 x2 4x 21 Write in standard form. 0 (x 3)(x 7) Factor. x 3 0 or x 7 0 Set each factor equal to zero. x 3 x 7 Solve. Step 5: Check the answer, and interpret the solution as it relates to the problem. We get two sets of solutions. If x 3, then the other odd integers are 1 and 1. If x 7, the other odd integers are 9 and 11. Check these numbers in the original statement of the problem. 23 (1) 1 (3)(1) 9 27 9 11 (7)(9) 9 2(3) 3 9 2(27) 63 9 6 6 54 54 In this application problem, one of the solutions is negative. Also note that this particular problem has two sets of solutions. YOU TRY 2 Solve. Find three consecutive even integers such that the product of the two smaller numbers is the same as twice the sum of the integers. 404 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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