One-fourth of a herd of camels is seen in a forest, twice the square root of the herd went to the mountains, and the remaining 15 camels were by the river. Find the total number of camels.

Introduction:This is a classic herd puzzle forming an equation with a square-root term. We translate the story into algebra and solve for the total.

Given Data / Assumptions:

• Total camels = x
• Forest: x/4
• Mountains: 2 * sqrt(x)
• River bank: 15

Concept / Approach:Set up x/4 + 2*sqrt(x) + 15 = x and solve for x ≥ 0. Prefer integer solutions relevant to counts.

Step-by-Step Solution:x/4 + 2*sqrt(x) + 15 = xRearrange: 2*sqrt(x) = (3/4)x − 15Trial or algebraic manipulation shows x = 36 satisfies: 36/4 + 2*6 + 15 = 9 + 12 + 15 = 36

Verification / Alternative check:Check nearby integers; only 36 balances the equation exactly.

Why Other Options Are Wrong:32, 34, 35 do not satisfy the equation when substituted.

Common Pitfalls:Algebraic mistakes while isolating sqrt(x); forgetting the integer and nonnegative context for a count of camels.

Final Answer:36