JAMB 2025 Mathematics · Question 1

P is partly constant and varies partly as Q. If P = 32 when Q = 16 and P = 20 when Q = 12, find P when Q = 28

Options

A.68
B.64
C.66
D.62

Answer: A. 68

Explanation written with AI and checked against the answer key

Analyze the question: "P is partly constant and varies partly as Q" means P = k + mQ, where k and m are constants. Concept: Partial variation gives a linear equation. Use the two given pairs to form simultaneous equations, find k and m, then substitute the new value of Q. Solution: P = k + mQ When P = 32, Q = 16: k + 16m = 32 ... (i) When P = 20, Q = 12: k + 12m = 20 ... (ii) Subtract (ii) from (i): 4m = 12 m = 3 Substitute into (ii): k + 36 = 20 k = -16 So the formula is P = 3Q - 16. Check with (i): 3(16) - 16 = 48 - 16 = 32 ✓ Now find P when Q = 28: P = 3(28) - 16 = 84 - 16 = 68 Answer: P = 68, which is option A. Tip: For "partly constant and partly varies as" questions, always start with P = k + mQ. Subtracting the two equations eliminates k quickly. Always verify with one of the original pairs.

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