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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 9.69 (page 909)

The product of two consecutive odd integers is 99. Find the integers.

Short Answer

Expert verified

Two consecutive odd integers whose product is 99 are 9, 11 and $- 9, - 11$ .

Step by step solution

01

Step 1. Form a quadratic equation.

It is given that the product of two consecutive odd integers is 99.

Let $n$ be the first odd integer and $n + 2$ is the second odd integer. Then,

$\begin{array}{rcl} n (n + 2) & = & 99 \\ n^{2} + 2 n - 99 & = & 0 \end{array}$

02

Step 2. Solve the equation.

Split the middle term.

$\begin{array}{rcl} n^{2} + 11 n - 9 n - 99 & = & 0 \\ n (n + 11) - 9 (n + 11) & = & 0 \\ (n - 9) (n + 11) & = & 0 \\ n & = & 9 and n = - 11 \end{array}$

03

Step 3. Determine the second odd integer.

For $n = 9$ ,

$\begin{array}{rcl} n + 2 & = & 9 + 2 \\ = & 11 \end{array}$

For $n = - 11$

$\begin{array}{rcl} n + 2 & = & - 11 + 2 \\ = & - 9 \end{array}$

04

Step 4. Conclusion.

Two consecutive odd integers whose product is 99 are 9, 11 and $- 9, - 11$ .

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