To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. From an average lemon one can squeeze out 0.4 cups of 5% citric acid. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. If she has sugar and water in abundance, how much water will Marta use?

She will need to add 5.6 cups of water

Explanation:

Hi there!

Marta has to dilute the citric acid to 5%.

The dilution factor will be 12% / 5% = 2.4. Then, Marta will need to dilute the citric acid 2.4 times. If she has 4 cups of the solution, she will need to add water until she completes a volume of (4 cups ·2.4) 9.6 cups to reach the desired concentration.

Then, she will need to add 9.6 - 4 cups water = 5.6 cups of water

Another way to solve this is by using the fact that the mass of citric acid in the concentrated and diluted solution is the same. Then:

mass citric acid concentrated solution = mass citric acid in dilute solution

mass of citric acid = concentration · volume

Then:

initial concentration · volume = final concentration · volume

12% · 4 cups = 5% · volume

volume = 12% · 4 cups / 5% = 9.6 cups

The final volume of the solution at 5% will be 9.6 cups. So Marta will need 9.6 cups - 4 cups = 5.6 cups water