Total amount of the mixture = [tex] 10\frac{1}{2}=10.5 [/tex] ounces
Proportion of formula = [tex] \frac{1}{3} [/tex]
Proportion of water = [tex] \frac{2}{3} [/tex]
Amount of water needed to make the mixture can be given as:
Total amount of mixture x Proportion of water
Using the values, we get:
Amount of water needed = [tex] 10.5*\frac{2}{3} [/tex] = 7 ounces
Similarly the amount of formula needed will be:
Total amount of mixture x Proportion of formula
Using the values, we get:
Amount of formula needed = [tex] 10.5*\frac{1}{3} [/tex] = 3.5 ounces
Therefore, the home health care assistant needs 3.5 ounces of formula and 7 ounces of water to prepare 10 and a half ounces of formula.