A farmer has hens and cows. The total number of heads is 48 and the total number of feet is 140. How many hens are there?

Introduction / Context:
This is a classic heads-and-legs (feet) problem using simultaneous linear equations. Each animal contributes 1 head; hens have 2 feet and cows have 4 feet.

Given Data / Assumptions:

• Total heads = 48 (hens + cows).
• Total feet = 140.
• Hens have 2 feet; cows have 4 feet.

Concept / Approach:
Let h = number of hens, c = number of cows. Form two equations: h + c = 48 and 2h + 4c = 140. Solve the system to find h.

Step-by-Step Solution:
h + c = 48. 2h + 4c = 140 ⇒ divide by 2 ⇒ h + 2c = 70. Subtract: (h + 2c) − (h + c) = 70 − 48 ⇒ c = 22. Then h = 48 − 22 = 26.

Verification / Alternative check:
Check feet: 26 hens ⇒ 52 feet; 22 cows ⇒ 88 feet; total 52 + 88 = 140. Correct.

Why Other Options Are Wrong:
22 or 23 or 24 hens do not simultaneously satisfy both equations.

Common Pitfalls:
Mixing up the number of feet per animal or making arithmetic slips while subtracting equations. Use systematic elimination to avoid errors.

Final Answer:
26