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WAEC 2018 Mathematics · Question 28

If x : y : z = 3 : 3 : 4, evaluate 9x+3y6z−2y\frac{9x + 3y}{6z - 2y}

Options

  1. A.112\frac{1}{2}
  2. B.2
  3. C.212\frac{1}{2}
  4. D.3

Answer: B. 2

Explanation written with AI and checked against the answer key

Analyze the question: We're given the ratio x : y : z = 3 : 3 : 4 and must evaluate (9x + 3y)/(6z − 2y). Concept: If x : y : z = 3 : 3 : 4, we can write x = 3k, y = 3k, z = 4k for some constant k (k ≠ 0). The k will cancel out in the final fraction. Solution: Numerator: 9x + 3y = 9(3k) + 3(3k) = 27k + 9k = 36k Denominator: 6z − 2y = 6(4k) − 2(3k) = 24k − 6k = 18k Fraction: (36k)/(18k) = 2 Answer: The value is 2, which is option B. Tip: For ratio questions like this, always replace the variables with a common multiple (3k, 3k, 4k). The k cancels, and you avoid guessing numbers. You can also just use k = 1: x = 3, y = 3, z = 4, giving (27 + 9)/(24 − 6) = 36/18 = 2.

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