AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 17

3 marks · Medium difficulty · Reasoning

Determine which packet of rice is better value for money by comparing costs per mass or mass per cost: Packet A (200 g for £1.10) or Packet B (500 g for £2.60).

Practise this question

Question

Question 17 shows illustrations of two packets of rice labelled A and B. Packet A costs £1.10 for 200 g. Packet B costs £2.60 for 500 g. The question asks: 'Which packet of rice is better value for money? Tick a box: A or B. You must show your working.' Worth 3 marks.

Mark scheme

Show the mark scheme Mark scheme for Question 17 outlining two main methods: Alternative method 1 finds comparable costs or masses (e.g. cost of 100 g: 55p for A vs 52p for B; or 1 kg: £5.50 vs £5.20) to award M1 for finding cost/mass of one, M1dep for both comparable values, and A1 for choosing Packet B with correct values. Alternative method 2 scales up or down directly by finding scale factors. Additional guidance clarifies acceptable comparison methods and units.

How to answer it

Comparing 'Value for Money' (Unit Pricing)

📋 What this question tests

This question assesses your ability to solve proportion problems in a real-life context: finding unit costs or scaling to a common mass/cost to determine which item offers the best value for money, followed by writing a clear conclusion supported by evidence.

Question 17 (3 marks)

Packet A: 200 g for £1.10  |  Packet B: 500 g for £2.60

✅ Final Answer

Packet B is better value for money.

Box B must be ticked, supported by two correct, comparable values (e.g. 55p vs 52p per 100 g).

💡 Key Knowledge

  • Fair Comparison: You cannot compare £1.10 and £2.60 directly because the masses are different. You must convert both to the same mass or the same cost.
  • Common Targets:
    • Cost per 100 g (easiest numbers to work with)
    • Cost per 1 kg (1000 g)
    • Cost per 1 g, or grams per £1
    • Scaling Packet A up to 500 g

📐 Step-by-Step Methods to Score Full Marks

Method 1: Find the Cost of 100 g for Both Packets (Recommended)
  1. Packet A (200 g = £1.10 or 110p):
    Divide by 2: 110p ÷ 2 = 55p per 100 g (or £0.55 ).
  2. Packet B (500 g = £2.60 or 260p):
    Divide by 5: 260p ÷ 5 = 52p per 100 g (or £0.52 ).
  3. Comparison & Conclusion:
    52p is less than 55p, so Packet B is cheaper per 100 g. Tick B.
Method 2: Scale up to a Common Mass of 1000 g (1 kg)
  1. Packet A: 200 g × 5 = 1000 g → £1.10 × 5 = £5.50
  2. Packet B: 500 g × 2 = 1000 g → £2.60 × 2 = £5.20
  3. Conclusion: £5.20 < £5.50, so Packet B is better value.
Method 3: Scale Packet A directly to 500 g
  1. Find cost of 500 g of Packet A: £1.10 × 2.5 = £2.75
  2. Packet B costs £2.60 for 500 g.
  3. Conclusion: Packet B costs £2.60 compared to £2.75 for the same amount, so Packet B is better value.
Mark Breakdown:
• M1: Correct method to find the cost of any common mass for either packet (e.g. 1.10 ÷ 2 or 2.60 × 2 ).
• M1 (dep): Fully correct method or values for both packets that allow a direct comparison (e.g. 55p and 52p, or £5.50 and £5.20).
• A1: Packet B identified with clear, correct supporting values.

🧠 Exam Technique & Examiner Commentary

  • Always state the units: Working in pence (e.g. 55p and 52p) avoids messy decimal places and reduces arithmetic slips.
  • No tick without working: Just ticking box B without valid mathematical working scores 0 marks. You must show working.
  • Clear labels: Clearly label your working with "Packet A" and "Packet B" so the examiner can follow your method instantly.

❌ Common Errors to Avoid

  • Comparing without common units: Saying "Packet A is cheaper because £1.10 is less than £2.60" completely ignores the different weights.
  • Rounding too early: Calculating price per 1 g gives £0.0055 and £0.0052 . If you round both to 1p, you cannot make a comparison and lose the final mark!
  • Inverting the division: Dividing mass by price (e.g. 200 ÷ 1.10 = 181.8 g per £1 ) is mathematically valid, but remember: for grams per pound, more is better, whereas for pence per gram, less is better. Mixing these up leads to wrong conclusions.

Topics

Ratio, proportion and rates of change · Number · 3.3 Ratio, proportion and rates of change · 3.1.1 Structure and calculation

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 2 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.