WAEC 2013 Mathematics · Question 27

If y varies directly as the square root of (x + 1) and y = 6 when x = 3, find x when y = 9

Options

Answer: A. 8

Explanation written with AI and checked against the answer key

Analyze the question: "y varies directly as the square root of (x + 1)" means y = k√(x + 1), where k is a constant. Step 1: Find k When x = 3, y = 6: 6 = k√(3 + 1) = k√4 = 2k k = 3 Step 2: Write the equation y = 3√(x + 1) Step 3: Find x when y = 9 9 = 3√(x + 1) √(x + 1) = 3 x + 1 = 9 x = 8 Check: √(8 + 1) = √9 = 3, and 3 × 3 = 9 ✓ Answer: x = 8, which is option A. Tip: For direct variation problems, always follow these steps: (1) write the equation with k, (2) use the first pair of values to find k, (3) substitute k and the second value. You can also use the ratio method: y₁/y₂ = √(x₁+1)/√(x₂+1) → 6/9 = 2/√(x+1) → √(x+1) = 3. Both methods give the same result.

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