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WAEC 2020 Mathematics · Question 48

A man is five times as old as his son. In four years' time, the product of their ages would be 340. If the…

Question

A man is five times as old as his son. In four years' time, the product of their ages would be 340. If the son's age is y, express the product of their ages in terms of y.

  1. A.5y2−16y−380=0^2 - 16y - 380 = 0
  2. B.5y2−24y−380=0^2 - 24y - 380 = 0
  3. C.5y2−16y−330=0^2 - 16y - 330 = 0
  4. D.5y2+24y−324=0^2 + 24y - 324 = 0

Answer: D. 5y2+24y−324=0^2 + 24y - 324 = 0

Explanation written with AI and checked against the answer key

Analyze the question: The son's age is y, so the man's age is 5y. In four years, their ages will be (y + 4) and (5y + 4), and the product of these is 340. Concept: Write each future age as "present age + 4", multiply, set the product equal to 340, then expand and rearrange into the form ay² + by + c = 0. Solution: (y + 4)(5y + 4) = 340 Expand: 5y² + 4y + 20y + 16 = 340 5y² + 24y + 16 = 340 Subtract 340 from both sides: 5y² + 24y + 16 − 340 = 0 5y² + 24y − 324 = 0 Check against the options: This matches option D exactly. Options A, B and C each have a negative y-coefficient or a constant of −380 or −330, none of which come from this expansion. (As a quick sanity check, solving gives y = 6: (6 + 4)(30 + 4) = 10 × 34 = 340 ✓. Also 5(36) + 24(6) − 324 = 180 + 144 − 324 = 0 ✓.) Answer: D. Tip: For "in n years' time" age problems, add n to each person's current age before doing anything else. Don't add n to the product. Then expand carefully, since the middle term comes from combining the two cross-products (4y + 20y = 24y).

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