How many mL of the 90% solution will I need to add to obtain the desired solution? What are the steps to solving this kind of equation?

Question

You need a 55% alcohol solution. On hand, you have a 210 mL of a 5% alcohol mixture. You also have 90% alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?

Answer 1

Let x = ml of 90% solution to be added

Then { (210)(5) + (x)(90) }/(x + 210) = 90

or 55x + 11,550 = 1050 + 90x

and 35x = 10,500

x = 300 ml of the 90% solution is needed.