You need a 40% alcohol solution. On hand, you have a 75 mL of a 30% alcohol mixture.

Question

You need a 40% alcohol solution. On hand, you have a 75 mL of a 30% alcohol mixture. You also have 45% alcohol mixture. How much of the 45% mixture will you need to add to obtain the desired solution?

You will need

 mL of the 45% solution

Answer 1

Hey Sunshine,

If you have 75 mL of a 30% alcohol mixture, then (75mL)(0.30) = 22.5 mL of that solution is alcohol.

Similarly, if you have x mL of a 45% alcohol mixture, then (x mL)(0.45) = 0.45x mL of that solution is alcohol.

When you combine these two liquids, you will have (75 + x) mL of liquid and you want it to be 40% alcohol.

So, you simply need to solve the equation:

75(0.30) + x(0.45) = (75 + x)(0.40)

22.5 + 0.45x = 30 + 0.40x (distribute the 0.40)

0.05x = 7.5 (subtract 22.5 from both sides and subtract 0.40x from both sides)

x = 150

So, you have to add 150 mL of the 45% solution.

Hope this helps! :)