you need a 10% alcohol solution. on hand, you have a 80ml of a 95% alcohol mixture. how much pure water will you need to add to obtain the desired solution.

Let x be the amount of pure water (in mL) you need to add. The new mixture would have a total volume of 80+x mL. The solution you have contributes 0.95 mL of alcohol for each mL of solution, so that it currently contains 0.95*80 = 76 mL of alcohol. You want to the new mixture to have a concentration of 10%, so that

76 / (80 + x) = 0.1

==> 76 = 0.1 (80 + x) = 8 + 0.1x

==> 68 = 0.1x

==> x = 680 mL