WAEC 2023 Mathematics · Question 15

M varies jointly as the square of n and square root of q. If M = 24 when n = 2 and q = 4, find M when n = 5, q = 9.

Options

A.288
B.400
C.300
D.225

Answer: D. 225

Explanation written with AI and checked against the answer key

Analyze the question: "Varies jointly" means M is proportional to the product of the given quantities: M ∝ n² × √q. Concept: Joint variation gives M = k·n²·√q, where k is a constant. Step 1: Find k M = 24, n = 2, q = 4 24 = k × (2²) × √4 24 = k × 4 × 2 24 = 8k k = 3 Step 2: Find M when n = 5, q = 9 M = 3 × 5² × √9 M = 3 × 25 × 3 M = 225 Answer: M = 225, which is option D. Tip: For joint variation, always write the full equation first (M = k·n²·√q), find k using the first set of values, then substitute the second set. Be careful to apply the square to n and the square root to q, not the other way around.

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