Three consecutive odd numbers, sum condition: The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number?

Introduction / Context:
Problems with consecutive integers are easily modeled using algebra. Represent consecutive odd numbers as n, n + 2, n + 4, and translate the sum condition into an equation.

Given Data / Assumptions:

• First odd = n
• Second odd = n + 2
• Third odd = n + 4
• Sum = n + (n + 2) + (n + 4) = 20 + n

Concept / Approach:
Set up and solve the linear equation from the stated condition. The middle number is then n + 2.

Step-by-Step Solution:
3n + 6 = n + 202n = 14 → n = 7Middle number = n + 2 = 9

Verification / Alternative check:
Check: 7 + 9 + 11 = 27, which is 20 more than the first (7 + 20 = 27). Condition satisfied.

Why Other Options Are Wrong:
7 is the first, not the middle; 11 and 13 do not match the derived middle given the condition; “Data inadequate” is incorrect because the information is sufficient.

Common Pitfalls:
Using n, n + 1, n + 2 instead of odd steps; forgetting the +2 pattern for odd numbers.

Final Answer:
9