Question
A 40-litre solution contains 35% acid. How many litres of a 55% acid solution must be added so that the resulting mixture contains 45% acid?
Solution
Let x = litres of 55% solution added. Acid in first solution = 35% of 40 = 14 L Acid in second solution = 55% of x = 0.55x Total acid = 14 + 0.55x Total volume = 40 + x Required concentration: 45% ⇒ (14 + 0.55x) / (40 + x) = 0.45 14 + 0.55x = 0.45(40 + x) 14 + 0.55x = 18 + 0.45x 0.55x − 0.45x = 18 − 14 0.10x = 4 ⇒ x = 40 L Answer: 40 litres of 55% solution must be added.
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