Mixture Problem, please help!

Question

You need a 90% alcohol solution. On hand, you have a 140 mL of a 20% alcohol mixture. How much pure alcohol will you need to add to obtain the desired solution?

 

I need 980 mL of pure alcohol 

to obtain
________mL of the desired 90% solution.

Answer 1

You have to add 980mL alcohol so the total volume will be 140+980=1120mL. The amount of alcohol is .2*140 + 980 = 1008mL. The percentage is 1008/1120=.9 = 90% so that you need the entire 980mL to get the desired solution. Another better and more general solution method is to let the amount to added be x. Then 140*.2 + x*1. = (140+x)*.9. With .2=20%, 1=100%, .9=90%. With alcohol on the left and volume on the right side of the equation. Solving for x gives

x=980mL to be added which corresponds to the first answer. However Brooke, to nitpick, this solution is not exact as adding alcohol to water changes the volume.