At a marriage party, 32% are women, 54% are men, and there are 196 children. How many men are present at the party?

Introduction:
This question mixes percentages with an absolute headcount to find the total and then the number of men. Recognizing that all groups are percentages of the same total lets us back out the total from the known count of children.

Given Data / Assumptions:
Women = 32% of total. Men = 54% of total. Children = remainder = 100% − (32% + 54%) = 14% of total. Children count = 196 (absolute).

Concept / Approach:
If 14% corresponds to 196, then total attendees T satisfy 0.14 * T = 196. Solve for T, then compute 54% of T to get the number of men.

Step-by-Step Solution:
0.14 * T = 196 ⇒ T = 196 / 0.14 = 1400. Men = 54% of 1400 = 0.54 * 1400 = 756.

Verification / Alternative check:
Women = 32% of 1400 = 448. Children = 14% of 1400 = 196. Check: 448 + 756 + 196 = 1400, which matches the total.

Why Other Options Are Wrong:
448: That is the number of women (32% of 1400), not men. 332 and 324: Do not equal 54% of the computed total. 672: Corresponds to 48% of 1400, not the given 54% for men.

Common Pitfalls:
Using 196 as 32% or 54% mistakenly, or adding percentages incorrectly. Always ensure percentages sum to 100% and identify which share matches the given absolute count.

Final Answer:
The number of men present is 756.