AQA GCSE Mathematics Paper 3 (Higher), June 2025: Question 9

3 marks · Medium difficulty · Multi-step Problem

Calculate how much money Ary has given that Cat has £280, Cat's amount is 2/3 of Bea's amount, and the ratio of Ary's amount to Bea's amount is 5 : 12.

Practise this question

Question

Question 9 states: Ary, Bea and Cat each have an amount of money. Cat has £280. Cat's amount is 2/3 of Bea's amount. Ary's amount : Bea's amount = 5 : 12. Work out how much money Ary has. The question is worth 3 marks, with an answer line labelled 'Answer £'.

Mark scheme

Show the mark scheme Mark scheme for question 9 outlining two methods. Alternative method 1: 280 divided by 2 times 3 to find Bea's amount of 420 (M1), then 420 divided by 12 times 5 (M1 dependent), giving the final answer 175 (A1). Alternative method 2: 2/3 times 12 to find Cat's ratio part as 8 (M1), then 280 divided by 8 times 5 (M1 dependent), giving 175 (A1). Special case SC2 is given for using 2/3 of Cat's amount yielding 77.77 or 77.78.

How to answer it

Linking Fractions and Ratios: Sharing Money

📌 What this question tests

This question assesses your ability to solve multi-step problems linking fractions of an amount and ratio parts. Specifically, you need to work backwards from a known fractional value to find an original quantity, and then share or scale an amount using a given ratio ( Ary : Bea = 5 : 12 ).

Question 9 • 3 Marks

Problem Walkthrough & Working

Finding Ary's share from Cat's known amount

📐 Step-by-Step Calculations

Method 1: Find Bea's amount first (Recommended)

1 Find Bea's amount:
Cat has £280, which is 2/3 of Bea's amount.
2 parts = £280
1 part = 280 ÷ 2 = £140
Bea has 3 parts: 140 × 3 = £420

2 Find the value of 1 ratio part for Ary and Bea:
Ary : Bea = 5 : 12
Bea represents 12 parts = £420
1 part = 420 ÷ 12 = £35

3 Calculate Ary's amount:
Ary has 5 parts: 5 × £35 = £175

✅ Correct Answer & Marks

Answer: £175

Mark Scheme Breakdown:
  • M1: Finding Bea's total: 280 ÷ 2 × 3 or 420
  • M1dep: Scaling to Ary's share: their 420 ÷ 12 × 5
  • A1: Correct answer: 175 (units of £ already given)

💡 Alternative Method: 3-Way Ratio

You can also express all three people in a single combined ratio:

  • Ary : Bea = 5 : 12
  • Cat has 2/3 of Bea's amount:
    2/3 × 12 = 8 parts
  • Combined ratio: Ary : Bea : Cat = 5 : 12 : 8 (awards M1)
  • 8 parts = £280, so 1 part = 280 ÷ 8 = £35
  • Ary = 5 × £35 = £175 (awards M1dep A1)

🧠 Exam Technique & Examiner Insight

  • Identify the reference: Cat's amount is 2/3 of Bea's amount. That means Cat = 2 parts, Bea = 3 parts. Bea must have more money than Cat (£420 > £280).
  • Sense-check your numbers: In the ratio Ary : Bea = 5 : 12, Ary has less than half of Bea's money. Since Bea has £420, Ary having £175 makes intuitive sense.
  • Method Marks: Full method marks (M2) can be awarded for clear working even if a slip occurs in the final multiplication. Always show every calculation step!

❌ Common Errors to Avoid

  • Finding 2/3 of Cat instead of Bea: Calculating 280 × 2/3 ≈ £186.67 . This mistakes Cat's total for Bea's and leads to the incorrect answer £77.78 (earns only SC2).
  • Dividing Bea's total by 17: Adding the ratio parts ( 5 + 12 = 17 ) and doing 420 ÷ 17 . £420 belongs to Bea alone, so it must be divided by Bea's 12 parts only.
  • Inverting the ratio: Multiplying by 12 and dividing by 5, which would incorrectly give Ary more money than Bea.

Topics

Number · Ratio, proportion and rates of change · 3.1.2 Fractions, decimals and percentages · 3.3 Ratio, proportion and rates of change

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 3 (Higher), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.