WAEC 2019 Mathematics · Question 26

If 3p = 4q and 9p = 8q - 12, find the value of pq.

Options

A.12
B.7
C.-7
D.-12

Answer: A. 12

Explanation written with AI and checked against the answer key

Analyze the question: We have two equations in p and q. We solve them simultaneously, then multiply p and q. Concept: Use substitution. From the first equation, express one variable in terms of the other, then put it into the second. Solution: Equation 1: 3p = 4q, so p = 4q/3 Equation 2: 9p = 8q − 12 Substitute p = 4q/3 into Equation 2: 9(4q/3) = 8q − 12 12q = 8q − 12 4q = −12 q = −3 Now find p: 3p = 4(−3) = −12 p = −4 Check in Equation 2: 9(−4) = −36, and 8(−3) − 12 = −24 − 12 = −36 ✓ Now compute pq: pq = (−4)(−3) = 12 Answer: The correct option is A. **Tip: When one equation is a simple proportion like 3p = 4q, substitute straight into the other equation. Always check your values in both equations, and remember that a negative times a negative gives a positive, a common place to lose marks.

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