Question

You need a 45% alcohol solution. On hand, you have a 175 mL of a 25% alcohol mixture. You also have 70% alcohol mixture. How much of the 70% mixture will you need to add to obtain the desired solution?

Answer 1

175 mL at 25% concentration of alcohol contains 0.25 (175 mL) = 43.75 mL of alcohol. If v is the amount of the 70% solution that you use, then that amount contains 0.7v mL of alcohol.

Mixing these two yields a total volume of 175 mL + v, and it contains 43.75 mL + 0.7v alcohol. You want to end up with a concentration of 45%, which means the ratio of the amount of alcohol to the total volume needs to be 0.45:

(43.75 mL + 0.7v) / (175 mL + v) = 0.45

Solve for v :

43.75 mL + 0.7v = 0.45 (175 mL + v)

43.75 mL + 0.7v = 78.75 mL + 0.45v

0.25v = 35 mL

v = 140 mL