Three consecutive even numbers, sum equals a fraction of 176 minus 14: The sum of three consecutive even numbers is 14 less than one-fourth of 176. What is the middle number?

Introduction / Context:
This problem involves setting up consecutive even integers and equating their sum to a numerical expression derived from 176. Careful handling of the phrase “14 less than one-fourth of 176” is key.

Given Data / Assumptions:

• Numbers: n, n + 2, n + 4 (all even)
• One-fourth of 176 = 44; sum = 44 − 14 = 30

Concept / Approach:
Form the sum equation and solve for n. The middle number is n + 2.

Step-by-Step Solution:
n + (n + 2) + (n + 4) = 303n + 6 = 30 → 3n = 24 → n = 8Middle number = n + 2 = 10

Verification / Alternative check:
Numbers are 8, 10, 12 with sum 30. One-fourth of 176 is 44; 44 − 14 = 30. Condition holds.

Why Other Options Are Wrong:
6 and 8 are not the middle term; 12 is the largest; “Data inadequate” is invalid as the information is sufficient.

Common Pitfalls:
Interpreting “14 less than one-fourth of 176” incorrectly as 14 less than 176/4 after other operations; compute 176/4 first, then subtract 14.

Final Answer:
10