AlgebraVery hardAdding pure juice to a mixture
Algebra practice question
A 12-litre drink is 25% juice by volume. How many litres of pure juice must be added so that the drink is 40% juice?
Answer: 3
The drink has 0.25 × 12 = 3 litres of juice. Adding x litres of pure juice: (3 + x)/(12 + x) = 0.4, so 3 + x = 4.8 + 0.4x, 0.6x = 1.8, x = 3. Check: 6 litres of juice in 15 litres is 40%.
Common wrong answers
- If you answered 6
- 6 is the total juice in the final mixture (40% of 15 litres), not the amount added; 3 litres were already there.
- If you answered 1.8
- 1.8 is 0.15 × 12 — the extra 15% of the ORIGINAL volume. But adding juice also increases the total volume, so more is needed.
- If you answered 4.8
- 4.8 is 40% of 12, the juice a 12-litre drink would need — but the drink grows as juice is added.
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