The product of Rehan's age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age. Find his present age.
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
Let Rehan's present age = $x$ years.
Age 5 years ago = $(x - 5)$; age 7 years from now = $(x + 7)$.
Given: $(x - 5)(x + 7) = 2x + 1$
$x^2 + 2x - 35 = 2x + 1$
$x^2 = 36$
$x = 6$ (age cannot be negative)
Rehan's present age is 6 years.
Source: Chapter 4, Section 4.3
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Explanation
- Set up the equation directly from the word problem — this is the key skill tested.
- After expanding and simplifying, the $2x$ terms cancel, leaving $x^2 = 36$, giving $x = ±6$. Reject $x = -6$ (age must be positive).
- Show each step clearly; examiners award marks for correct equation formation (1 mark) and correct solution (1 mark).