Question

You need a 70% alcohol solution. On hand, you have a 150 mL of a 15% alcohol mixture. How much pure alcohol will you need to add to obtain the desired solution?

Answer 1

Answer: you have to add 60 mL of the 70% solution.

Explanation:

If you have 180 mL of a 30% alcohol mixture, then (180mL)(0.30) = 54mL of that solution is alcohol.

Similarly, if you have x mL of a 70% alcohol mixture, then (x mL)(0.70) = 0.70x mL of that solution is alcohol.

When you combine these two liquids, you will have (180 + x) mL of liquid and you want it to be 40% alcohol.

So, you simply need to solve the equation:

180(0.30) + x(0.70) = (180 + x)(0.40)

54 + 0.70x = 72 + 0.40x (distribute the 0.40)

0.30x = 18 (subtract 54 from both sides and subtract 0.40x from both sides)

x = 60

So, you have to add 60 mL of the 70% solution.

Hope this helps! :)