Mixing Paints in the Perfect Proportion

Understanding ratios can be tricky until you see how marks are awarded for each step in an exam-style question. Below is a 4-mark question aimed at a Foundation student who is still finding the idea of “parts” confusing. We also show how to structure your answer to secure full marks, and highlight common errors to avoid.

Question (4 marks)
A decorator needs to mix white and blue paint in the ratio 3 : 1 to make a pale blue finish.
(a) If she wants 8 litres of pale blue paint in total, how many litres of white paint and how many litres of blue paint should she use? (3 marks)
(b) Explain briefly why we divide by the total number of parts before multiplying. (1 mark)

Structured Answer and Mark Scheme

Part (a) – 3 marks

1. Identify total parts (1 mark)
   • 3 (white) + 1 (blue) = 4 parts.
2. Find value of one part (1 mark)
   • Total paint ÷ total parts = 8 L ÷ 4 = 2 L.
3. Scale each colour (1 mark)
   • White: 3 parts × 2 L = 6 L
   • Blue: 1 part × 2 L = 2 L

Part (b) – 1 mark
• Because we need to find the amount represented by one “part” before multiplying by 3 or 1.

Common Errors
• Reversing the colours (e.g. treating 3 parts as blue).
• Forgetting to add the parts to get 4 before dividing.
• Multiplying 8 L by 3 directly and giving 24 L of white paint.
• Omitting the explanation step, losing the final mark.

If you’re finding ratio setups confusing, targeted support—such as GSCE Maths Tutoring—will help you nail each step and boost your confidence.