1Cademy - Solving for Two Consecutive Odd Integers Whose Product is $$483$$

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Problem-Solving Strategy for Word Problems

Example

Solving for Two Consecutive Odd Integers Whose Product is $483$

Apply the problem-solving strategy to find two consecutive odd integers whose product is $483$ .

Let $n$ represent the first odd integer, which means the next consecutive odd integer is $n + 2$ . The equation for their product is: $n(n + 2) = 483$ . Distribute $n$ to obtain $n^2 + 2n = 483$ . Convert the equation to standard quadratic form by subtracting $483$ from both sides: $n^2 + 2n - 483 = 0$ . Factor the resulting trinomial to find $(n - 21)(n + 23) = 0$ . Applying the Zero Product Property yields two possible values for the first integer: $n = 21$ and $n = -23$ .