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St Nicholas 2025 P6 Maths Prelim — Paper 2 Q11 Solution

Paper 2 · Q11 · 3 marks · Money

Question

A file cost \$3.10 more than a pen. Hakim bought twice as many pens as files. He spent a total of \$92.70. He spent \$6.30 more on the files than on the pens. Find the total cost of a pen and a file.
Answer: $7.90

Worked solution

  1. Money spent on files $= (92.70 + 6.30) \div 2 = \$49.50$
  2. on pens $= \$92.70 - \$49.50 = \$43.20$. Let there be $f$ files and $2f$ pens. Pen price $= \frac{43.20}{2f} = \frac{21.60}{f}$. Since each file costs \$3.10 more, $f \times (\frac{21.60}{f} + 3.10) = 49.50$, so $21.60 + 3.10f = 49.50$ and $f = 9$. Pen $= 21.60 \div 9 = \$2.40$
  3. file $= 2.40 + 3.10 = \$5.50$. Total $= 2.40 + 5.50 = \$7.90$.

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