WAEC 2011 Mathematics · Question 39

in a quiz competition, a student answers n questions correctly and was given D(n + 50) for each question…

Question

in a quiz competition, a student answers n questions correctly and was given D(n + 50) for each question correctly answered. If he gets D600.00 altogether, how many questions did he answer correctly?

A.18
B.15
C.12
D.10

Answer: D. 10

Explanation written with AI and checked against the answer key

Analyze the question: The student answers n questions correctly. Each correct answer earns D(n + 50)... but the wording is likely from the original, which reads "D(n + 50)" as the amount per question. Total = n(n + 50) = 600. Concept: Total money = (number of questions) × (amount per question). This gives a quadratic equation. Solution: n(n + 50) = 600 n² + 50n − 600 = 0 Factorise: we need two numbers that multiply to −600 and add to 50. These are 60 and −10. (n + 60)(n − 10) = 0 n = −60 (rejected, since the number of questions can't be negative) or n = 10. Check: 10 × (10 + 50) = 10 × 60 = 600 ✓ Tip: In word problems that lead to quadratics, always reject negative values when counting objects. You can also test the options quickly: substitute each into n(n + 50) and see which gives 600.

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