AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 22

4 marks · Medium difficulty · Multi-step Problem

Calculate the total number of adults in a group visiting a theme park given ticket prices, an offer of one adult free with every 5 students, the number of students, and the total cost.

Practise this question

Question

Question 22 states: 'A group of adults and students go to a theme park. Here are the prices: Adult £24.50, Student £16.25, One adult free with every 5 students. In the group there are 48 students. The total price for the group is £927. How many adults are in the group?' It includes space for working and an answer line, worth 4 marks.

Mark scheme

Show the mark scheme Mark scheme for question 22: First mark M1 for 48 × 16.25 or 780. Second mark M1dep for (927 − their 780) ÷ 24.50 or 147 ÷ 24.50 or 6. Third mark M1 for 48 ÷ 5 or 9(.6) or 9r3. Final mark A1 for 15. Special cases SC3 for 63, SC2 for 54 or 57.

How to answer it

Theme Park Group Tickets: Working Out Total Adults

What this question tests

This multi-step problem tests your ability to deconstruct a real-life pricing scenario involving conditional discounts:

  • Calculating total cost for a known subgroup using unit prices.
  • Subtracting known costs to isolate remaining amounts.
  • Integer division with remainders in context (identifying "free" allowances).
  • Synthesising two separate quantities (paying adults + free adults) to find the final total.
Question 22 • [4 Marks]

Full Question Walkthrough

Calculate the total number of adults in the theme park group

📐 Step-by-Step Calculation

  1. Cost of the 48 students:
    48 × £16.25 = £780
  2. Cost paid for adults:
    £927 − £780 = £147
  3. Number of paying adults:
    £147 ÷ £24.50 = 6 paying adults
  4. Number of free adults:
    1 free adult for every 5 students.
    48 ÷ 5 = 9.6 → 9 free adults (you cannot have a fraction of a free adult, 3 students left over do not earn another free place).
  5. Total number of adults:
    6 (paying) + 9 (free) = 15 adults

✅ Correct Answer & Mark Scheme Breakdown

  • M1: Finding total cost of students: 48 × 16.25 or 780 .
  • M1 (dep): Subtracting and dividing by adult price: (927 − 780) ÷ 24.50 or 6 .
  • M1 (ind): Calculating free adult quota: 48 ÷ 5 or finding 9 free adults (e.g. counting in 5s up to 45).
  • A1: Correct total: 15 .

🧠 Exam Technique & Strategy

  • Split the problem into two tracks: Track A calculates paying people from the money (£927); Track B calculates free people from the rules (48 ÷ 5).
  • Show intermediate labels: Write "Students cost = £780", "Paying adults = 6", and "Free adults = 9". If you slip up on mental arithmetic, having labelled steps guarantees method marks.
  • Notice independent marks: Even if you make an error on the money side, writing 48 ÷ 5 = 9 scores an independent M1.

❌ Common Traps & Misconceptions

  • Stopping at 6: Many candidates correctly work out £147 ÷ £24.50 = 6, but forget to add the 9 free adults.
  • Rounding 9.6 up to 10: The park only gives 1 free ticket per complete block of 5 students. 48 contains 9 full blocks of 5 (with 3 remaining), so only 9 tickets are free.
  • Adding all group members: Writing 63 (48 students + 15 adults) answers "how many people in the group", not "how many adults". This scores a special case SC3.
  • Adding students to adults: Answering 54 (48 + 6) or 57 (48 + 9) scores SC2.
Examiner Insight: High-scoring students immediately separated the financial calculation from the "special offer" calculation before bringing them together at the final line. Losing the final mark by writing 6 was the single most frequent error on this question.

Topics

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

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.