AlgebraHardStrengthening a mixture
Algebra practice question
A 5-litre drink is 20% juice. How many litres of pure juice must be added so that the drink becomes 50% juice?
Answer: 3
The drink has 1 litre of juice. (1 + x)/(5 + x) = 1/2 gives 2 + 2x = 5 + x, so x = 3.
Common wrong answers
- If you answered 5
- 5 litres added would give 6/10 = 60%.
- If you answered 1.5
- 1.5 makes 30% of 5 litres, ignoring that the total also grows.
- If you answered 2.5
- 2.5 is half of 5, treating the added juice as if it didn't change the total.
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