AQA GCSE Mathematics Paper 3 (Foundation), June 2025: Question 8

3 marks · Easy difficulty · Multi-step Problem

Work out the cost of one hot dog given the cost of one burger and the total cost of two burgers and three hot dogs.

Practise this question

Question

Question 8 asks: One burger costs £3.80. Two burgers and three hotdogs cost £15.85. Work out the cost of one hot dog. There are lines for working out and an answer line stating 'Answer £' worth 3 marks.

Mark scheme

Show the mark scheme Mark scheme table for Question 8: M1 for '2 x 3.8(0) or 7.6(0)'; M1dep for '15.85 - their 7.6(0) or 8.25'; A1 for '2.75' (SC2 for 275). Additional guidance notes: condone £2.75p, and 7.60 - 15.85 unless recovered earns M1M0dep.

How to answer it

Solving Multi-Step Word Problems: Cost of Items

📋 What this question tests

This question assesses your ability to set up and solve a multi-step real-life arithmetic problem involving money. Specifically, it tests:

  • Multiplication of money/decimals: Calculating the total cost of multiple identical items.
  • Subraction in context: Finding the remaining balance for an unknown group of items.
  • Division to find a unit cost: Dividing the remaining balance equally among the number of items.
  • Money formatting: Expressing solutions correctly in standard currency notation (£).

Question 8

Full Question Walkthrough & Marks Breakdown (3 Marks)

📐 Step-by-Step Calculation

1 Find the total cost of the two burgers:
Cost = 2 × £3.80 = £7.60

2 Find the total cost of the three hot dogs:
Subtract the burger cost from the total spend:
£15.85 − £7.60 = £8.25

3 Find the cost of one hot dog:
Divide the remaining balance by 3:
£8.25 ÷ 3 = £2.75

✅ Correct Answer & Mark Allocation

Answer: £2.75

M1: For 2 × 3.80 or showing 7.60 (working in pence as 760 is accepted).
M1dep: Dependent on the first mark: for subtracting their cost of two burgers from 15.85 ( 15.85 − 7.60 or showing 8.25 ).
A1: For 2.75 .
Special Case: If a student writes 275 on the answer line with the £ symbol already present, award SC2.

💡 Key Knowledge

  • Algebraic Structure: You can think of this as a simple linear equation:
    2b + 3h = 15.85 where b = 3.80 .
  • Units consistency: You can work entirely in pounds (£15.85, £7.60) or entirely in pence (1585p, 760p), but never mix them up in the same calculation!
  • Decimal division: When dividing £8.25 by 3:
    8 ÷ 3 = 2 remainder 2 → 22 ÷ 3 = 7 remainder 1 → 15 ÷ 3 = 5, giving 2.75.

🧠 Exam Technique & Examiner Insight

  • Show all intermediate steps: Notice that the second mark ( M1dep ) depends on showing the method for two burgers first. Writing down 7.60 and 8.25 guarantees method marks even if a minor arithmetic slip occurs later.
  • Check units on the answer line: The exam paper provides the £ sign. If you calculate in pence (275p), remember to convert it to pounds ( 2.75 ) to avoid losing a precision mark.
  • Sensible answer check: A single hot dog costing £2.75 is realistic compared to a £3.80 burger. If your answer is £27.50 or £0.27, stop and re-check decimal placement!

❌ Common Errors to Avoid

  • Order of subtraction: Writing 7.60 − 15.85 = -8.25 loses the second method mark unless correctly recovered. Always subtract the smaller total from the grand total.
  • Dividing by the wrong quantity: Dividing £8.25 by 2 instead of 3 (confusing the number of burgers with the number of hot dogs).
  • Forgetting to multiply: Subtracting only one burger ( 15.85 − 3.80 ) instead of two. Read the bold words in the question carefully: Two burgers and three hot dogs.

Topics

Number · Algebra · 3.1.1 Structure and calculation · 3.2.3 Solving equations and inequalities

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