Question

A scientist has 40 liters of a 50% acidic solution. She adds a 20% acidic solution to create a mixture that has been diluted to have 30% acidity. The graph models the percent of acidity in the final mixture.
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How many liters of the 20% acidic solution should be added to create the needed 30% acidity in the final mixture?
0.5 liters
30 liters
80 liters
37 liters

Answer 1

Let x = liters of 20% solution added.

Acid amount initially = 0.50·40 = 20 liters.
Acid added = 0.20·x.
Total acid = 20 + 0.20x, total volume = 40 + x.

Set concentration to 30%:
(20 + 0.20x)/(40 + x) = 0.30
20 + 0.20x = 12 + 0.30x
8 = 0.10x → x = 80.

Answer: 80 liters.