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WAEC 2017 Mathematics · Question 34

Solve the equation: 15x+1x\frac{1}{5x} + \frac{1}{x}= 3

Options

  1. A.15\frac{1}{5}
  2. B.25\frac{2}{5}
  3. C.35\frac{3}{5}
  4. D.45\frac{4}{5}

Answer: B. 25\frac{2}{5}

Explanation written with AI and checked against the answer key

Analyze the question: We need to find x in 1/(5x) + 1/x = 3. Concept: To add fractions, use a common denominator. Here the common denominator is 5x. Solution: 1/(5x) + 1/x = 3 Rewrite 1/x with denominator 5x: 1/(5x) + 5/(5x) = 3 6/(5x) = 3 Cross-multiply: 6 = 15x x = 6/15 = 2/5 Check: x = 2/5, so 5x = 2, giving 1/2 + 1/(2/5) = 1/2 + 5/2 = 6/2 = 3 ✓ Answer: x = 2/5, which is option B. Tip: When an equation has fractions with x in the denominator, combine them over the common denominator first, then cross-multiply. Always substitute your answer back to confirm it.

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