how much water is needed to add to a half-pint of syrup with 60% sugar to obtain a drink with 5% sugar?

Answer 1

0.6*8 = 4.8 0z of sugar.
8-4.8 = 3.2 oz of water.

Sugar = 5%.
%Water = 100-5 = 95.

(3.2+w)/(4.8 + (w+3.2)) = 0.95
Cross multiply:
3.2+w = 4.56+0.95w+3.04
w-.95w = 4.56+3.04
0.05w = 7.6
W = 88 oz. of water added.