AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 8

3 marks · Easy difficulty · Multi-step Problem

Calculate the amount of lentils in grams needed to make lentil soup for 10 people given a recipe for 4 people.

Practise this question

Question

A table titled 'Lentil soup for 4 people' lists ingredients: Lentils 170 g, Water 600 ml, and Onion 50 g. Below the table, the question asks: 'How many grams of lentils are needed to make this soup for 10 people?' with an answer line specifying units of grams.

Mark scheme

Show the mark scheme Mark scheme for question 8 showing two alternative methods. Method 1 awards M2 for 170 ÷ 4 × 10 (or M1 for 170 ÷ 4 or 10 ÷ 4) and A1 for 425. Method 2 awards M1 for 170 ÷ 2 = 85, M1dep for 170 × 2 + 85, and A1 for 425. A special case SC2 awards 2 marks for 125 or 1500 (using onion or water quantities).

How to answer it

Proportion: Scaling Recipe Quantities

📋 What this question tests

This question assesses your ability to solve direct proportion problems in a practical context. Specifically, it tests:

  • Finding a scale factor or unitary amount (the amount for 1 person).
  • Scaling ingredients up from an original portion size (4 people) to a target portion size (10 people).
  • Selecting the correct ingredient and ignoring unnecessary numerical data.
Question 8 • 3 Marks

Scaling Lentils for 10 People

AQA Foundation / Higher Tier • Direct Proportion

💡 Key Knowledge: Proportion Methods

You can solve recipe proportion questions using any of these valid approaches:

  • Unitary Method: Find the quantity for 1 person first ( total ÷ 4 ), then multiply by 10.
  • Scale Factor Method: Find the multiplier to get from 4 to 10 ( 10 ÷ 4 = 2.5 ), then multiply the ingredient amount by 2.5.
  • Chunking / Building Blocks:
    • 4 people = 170 g
    • 8 people = 170 × 2 = 340 g
    • 2 people = 170 ÷ 2 = 85 g
    • 10 people = 8 people + 2 people = 340 + 85 = 425 g

📐 Step-by-Step Calculations

Method 1: Scale Factor

  1. Find the scale factor: 10 ÷ 4 = 2.5
  2. Multiply lentils by scale factor: 170 × 2.5 = 425 g

Method 2: Unitary Method

  1. Find lentils for 1 person: 170 ÷ 4 = 42.5 g
  2. Multiply by 10: 42.5 × 10 = 425 g

✅ Correct Answer & Mark Allocation

Final Answer: 425 g

Mark Breakdown:
• M1: Correct first step using one operation (e.g. 170 ÷ 4 , 10 ÷ 4 , 170 × 10 , or finding half 170 ÷ 2 = 85 )
• M2: Complete correct method (e.g. 170 ÷ 4 × 10 , 170 × 2.5 , or 170 × 2 + 85 )
• A1: Accurate final answer of 425

🧠 Exam Technique & Tips

  • Isolate the required ingredient: The question asks specifically for lentils (170 g). Ignore 600 ml water and 50 g onion!
  • Show all working: If you write down 170 ÷ 4 × 10 , you secure M2 immediately, protecting you against simple arithmetic errors.
  • Sense-check your answer: 10 people is 2.5 times as many as 4 people. Since 170 × 2 = 340 and 170 × 3 = 510 , your answer must be midway between 340 and 510.

❌ Common Errors & Examiner Insights

  • Using the wrong row in the table: A very common slip is calculating the proportion for water ( 600 × 2.5 = 1500 ) or onions ( 50 × 2.5 = 125 ). The mark scheme gives a special case mark ( SC2 ) for 125 or 1500, meaning students lose at least 1 mark simply for not reading the ingredient name carefully.
  • Additive instead of multiplicative thinking: Incorrectly thinking "to get from 4 people to 10 people, add 6, so add 6 g to 170 g". Quantities must be scaled multiplicatively!
  • Incomplete "building block" method: Finding 8 people (340 g) or 2 people (85 g) correctly, but failing to add them together to reach 10 people.

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 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.