The sum of two consecutive odd integers is $176$. Find the integers

• A. $83$ and $93$
• B. $87$ and $89$
• C. $85$ and $91$
• D. $84$ and $92$

Answer: (B)

Verified step by step guidance

1. Let the first odd integer be represented by the variable \(x\). Since the integers are consecutive odd integers, the next odd integer can be represented as \(x + 2\).
2. Write an equation expressing the sum of the two consecutive odd integers: \(x + (x + 2) = 176\).
3. Combine like terms on the left side of the equation: \$2x + 2 = 176$.
4. Isolate the variable term by subtracting 2 from both sides: \$2x = 176 - 2$.
5. Solve for \(x\) by dividing both sides by 2: \(x = \frac{176 - 2}{2}\). Then find the second integer by calculating \(x + 2\).