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St Nicholas 2025 P6 Maths Prelim — Paper 2 Q16a Solution

Paper 2 · Q16a · 3 marks · Algebra

Question

Paul and Zalim went out together with a total of \$140.20. Zalim spent 4 times as much money as Paul. The amount of money Paul had left was \$12 more than $\frac{1}{2}$ of what Zalim spent. The amount of money Zalim had left was $\frac{1}{5}$ of what Paul had left. (a) How much money did Paul spend?
Answer: $17

Worked solution

  1. Let Paul spend 1 unit, so Zalim spent 4 units. Paul left $= 2\text{ units} + \$12$ (half of Zalim's spending is 2 units). Zalim left $= \frac{1}{5}$ of Paul's left. Total money $= 1 + 4 + (2\text{ units} + 12) + \text{Zalim left} = \$140.20$. Solving, $37\text{ units} + \$12 + \$2.40 = \$140.20$, so $37\text{ units} = \$125.80$ and $1\text{ unit} = \$3.40$. Paul spent $5 \times \$3.40 = \$17$.

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