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

✅ Correct Answer

47

📐 Step-by-Step Deduction

1. Find the base total: 31 parts (sheep) + 47 parts (cows) = 78 parts.
2. Consider integer multiples: Animals must be whole numbers, so the total must be a multiple of 78:
   • 78 × 1 = 78
   • 78 × 2 = 156 (exceeds the limit)
3. Apply condition: Total < 100, so the multiplier must be 1.
4. Find cows: 47 × 1 = 47.

💡 Key Knowledge

• Order matters: The ratio is written sheep : cows = 31 : 47 . The first number belongs to sheep and the second to cows.
• Discrete quantities: You cannot have fractions of animals. The common multiplier must be an integer (1, 2, 3...).

❌ Common Errors

• Order reversal: Writing 31 instead of 47 by mixing up the order of sheep and cows.
• Overcomplicating: Attempting to divide 100 by 47 or trying algebraic substitution rather than noticing 78 is the only possible multiple under 100.

✅ Correct Answer

78

📐 Step-by-Step Calculation

1. Number of sheep = 31
2. Number of cows = 47
3. Total animals = 31 + 47 = 78

🧠 Exam Technique

• Sense Check: Check if your answer satisfies every condition in the question:
  • Are they in the ratio 31 : 47? Yes (31 and 47).
  • Is the total fewer than 100? Yes (78 < 100).
• Follow-through: Even if you were unsure of part (a), the total of the ratio parts (31 + 47) directly provides the answer to part (b).

❌ Common Errors

• Guessing 99: Choosing 99 just because it is the largest integer "fewer than 100", ignoring that 99 cannot be divided into 31 : 47.
• Arithmetic slips: Adding 31 + 47 incorrectly (e.g. writing 68 or 88).