nutrition scientists have determined that for long distance running in the desert, a drink containing 5.0 glycerol per 100 mL of water is ideal. convert this to ounces per quart. Round to two significant digits.

Answer 1

5g/100mL * 1oz/28.35g * 1000mL/L * 1L/1.057qt
= (5*1000)/(100*28.35*1.057) = 1.67 oz/qt

Answer 2

I assume you meant:
5.0 ml glycerol per 100 mL of water
So it just becomes a ration of 5 : 100 or 1 : 20

If I recall: 1 US quart = 32 US fluid ounces
or 1 Imperial quart = 40 Imperial ounces

Going with the US version:
32 ounces = 1 quart
so 1 ounce = 1/32 quarts
but for every ounce of glycerin we need 20 ounces of water
1 ounce of glycerin = 20(1/32) quarts of water
1 ounce of glycerin per .63 quarts of water
or
1.6 ounces of glycerin per 1 quart of water

or:
5 ml/100 ml = x ounces / 1 quart
5 ml/100 ml = x ounces / 32 ounces
5/100 = x/32
100x = 160
x = 1.6

so you need 1.6 quarts of water for 1 ounce of glycerin.

(why not just stick with the metric system ??? )