Heads and legs puzzle (equal cows and herdsmen): In a group with an equal number of cows and herdsmen, the total number of legs was 28 less than four times the number of heads. How many herdsmen are there?

Introduction / Context:This classic heads-and-legs problem is solved by translating the verbal conditions into linear equations. Equal counts of cows and herdsmen imply paired head counts but different per-head leg counts (cows have 4 legs; herdsmen have 2 legs).

Given Data / Assumptions:

• Let n be the number of cows and also the number of herdsmen.
• Total heads = cows + herdsmen = 2n.
• Total legs = 4n (cows) + 2n (herdsmen) = 6n.
• Legs are 28 less than 4 times the number of heads.

Concept / Approach:Write legs = 4*(heads) − 28. Substitute heads = 2n and legs = 6n to form a single linear equation in n and solve.

Step-by-Step Solution:

Verification / Alternative check:Heads = 2n = 28; 4*heads = 112. Legs = 6n = 84. 112 − 84 = 28, matching the condition exactly.

Why Other Options Are Wrong:

• 7, 10, 21, 28: Do not satisfy 6n = 8n − 28 when substituted.

Common Pitfalls:Assigning the same leg count to cows and herdsmen or forgetting that the phrase “equal number” applies to counts of individuals, not legs or heads.

Final Answer:14