AQA GCSE Mathematics Paper 3 (Foundation), June 2025: Question 11

3 marks · Easy difficulty · Multi-step Problem

Calculate the total number of plates bought for 20 tables with 6 plates per table plus an extra 70% for spares.

Practise this question

Question

Question 11 states: 'Paul buys plates for his cafe. The cafe has 20 tables. He buys 6 plates for each table plus an extra 70% for spares. Work out how many plates Paul buys in total.' A blank answer space for 3 marks is provided below.

Mark scheme

Show the mark scheme Mark scheme for Question 11: M2 for 0.7 multiplied by 6 multiplied by 20 or 84, or 1.7 multiplied by 6 multiplied by 20. Partial credit M1 for finding 6 multiplied by 20 (120), or 0.7 multiplied by 6 (4.2), or 0.7 multiplied by 20 (14), or 1.7 multiplied by 6 (10.2), or 1.7 multiplied by 20 (34). A1 for 204. Special case SC2 for 200 or 220 resulting from rounding plates per table.

How to answer it

Calculating Quantities with Percentages: Cafe Plates

📋 What this question tests
  • Multi-step problem solving: Interpreting practical worded contexts involving groups and rates.
  • Percentage of an amount: Finding a percentage (70%) of a calculated base number or using a decimal multiplier (1.7).
  • Percentage increase: Adding extra quantities to a baseline total.

Question 11 (3 Marks)

Paul buys plates for his cafe. The cafe has 20 tables. He buys 6 plates for each table plus an extra 70% for spares. Work out how many plates Paul buys in total.

📐 Step-by-Step Solutions

Method 1: Total first, then add 70%

  1. 1 Find baseline plates needed:
    20 tables × 6 plates = 120 plates
  2. 2 Calculate the extra 70% spares:
    70% of 120 = 0.7 × 120 = 84 spare plates
  3. 3 Calculate grand total:
    120 + 84 = 204 plates

Method 2: Multiplier method (Quickest)

  1. An increase of 70% corresponds to a multiplier of 1.70 .
  2. Total = 20 × 6 × 1.7 = 204

✅ Mark Scheme Breakdown

  • 204 [A1]
Mark Allocations:
  • M1: Finds baseline total (6 × 20 = 120), or calculates 70% of a single component (e.g. 0.7 × 6 = 4.2 or 0.7 × 20 = 14).
  • M2: Complete method to find 70% of the total (0.7 × 6 × 20 = 84) OR uses the full multiplier (1.7 × 6 × 20).
  • A1: Correct final answer of 204.
  • Special Case (SC2): Award 2 marks for 200 or 220 (obtained by prematurely rounding 10.2 plates per table to 10 or 11 plates).

💡 Key Knowledge

  • Percentage Multipliers: To find 70% of a quantity, multiply by 0.7 . To add 70% to a quantity in one go, multiply by 1.7 (since 100% + 70% = 170%).
  • Order of Operations in Multiplication: Multiplication is associative and commutative:
    20 × 6 × 1.7 = (20 × 6) × 1.7 = 20 × (6 × 1.7) All routes lead to the same answer if decimals aren't rounded early!

🧠 Exam Technique & Examiner Tips

  • Reread the final demand: The question asks for the total number of plates, not just the number of spares. An answer of 84 only gains method marks.
  • Keep full accuracy during working: If you calculate plates per table first (6 × 1.7 = 10.2), do not round to 10 or 11 mid-way. 10.2 × 20 gives the exact integer 204.
  • Write down intermediate values: Always write down 120 or 84 so that if you make an addition error at the end, you still secure the 2 method marks (M2).

❌ Common Errors to Avoid

  • Stopping at the extra spares: Writing 84 on the answer line. Remember to add it back to the original 120!
  • Premature rounding: Calculating 6 + 70% = 10.2 plates per table, then rounding to 10 plates (giving 200) or 11 plates (giving 220). While this gets SC2, it loses the final accuracy mark.
  • Adding 70 instead of 70%: Calculating 120 + 70 = 190. A percentage represents a proportion, not a fixed number of items.

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