Deepak keeps hens (2 legs each) and goats (4 legs each). If the total number of animal heads is 90 and the total number of legs is 248, how many goats does Deepak have?

Introduction: Classic heads-and-legs problems are solved using linear equations. Each animal contributes one head; hens contribute 2 legs and goats contribute 4 legs. Two equations quickly reveal the counts of each type.

Given Data / Assumptions:

• Total heads = 90 (hens + goats).
• Total legs = 248 (2 per hen, 4 per goat).
• Let h = hens, g = goats; both are nonnegative integers.

Concept / Approach: Use the system: h + g = 90 and 2h + 4g = 248. Divide the second by 2 to simplify, then eliminate h to solve for g.

Step-by-Step Solution:

Verification / Alternative check: Legs: 2*56 + 4*34 = 112 + 136 = 248, matches perfectly.

Why Other Options Are Wrong: 32, 36, 38 lead to leg counts not equal to 248; “Cannot be determined” is incorrect because the system has a unique integer solution.

Common Pitfalls: Forgetting each animal has one head; mixing leg coefficients; or not simplifying the equations.

Final Answer: 34