1Cademy - Solving for Two Consecutive Odd Integers Whose Product is $$255$$

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Problem-Solving Strategy for Word Problems

Example

Solving for Two Consecutive Odd Integers Whose Product is $255$

Apply the problem-solving strategy to find two consecutive odd integers whose product is $255$ .

Let $n$ be the first odd integer, making the next consecutive odd integer $n + 2$ . The product of the two integers is $255$ , leading to the algebraic equation: $n(n + 2) = 255$ . Expanding the left side yields $n^2 + 2n = 255$ . Subtract $255$ from both sides to convert the quadratic equation into standard form: $n^2 + 2n - 255 = 0$ . Factor the trinomial to get $(n - 15)(n + 17) = 0$ . Setting each factor to zero using the Zero Product Property gives the solutions $n = 15$ and $n = -17$ .