It takes 1/3 cups of powered punch mix to make 2/3 gallons of punch. If the recipe is for 1 gallon of punch, how much punch is need to make 1/4 the recipe ?

[tex]\dfrac{1}{8}[/tex]Step-by-step explanation:The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.Number of powered punch mix cups required to make [tex]\frac{2}{3}[/tex] gallons of punch is [tex]\frac{1}{3}[/tex]Number of powered punch mix cups required to make [tex]\frac{2}{3}[/tex] gallons of punch is [tex]\frac{3}{2}\times[/tex][tex]\frac{1}{3}[/tex]=[tex]\frac{1}{2}[/tex]Since the recipe is for [tex]1[/tex] gallon,[tex]\frac{1}{2}[/tex] powered punch mix cups are required to make the complete recipe.[tex]\frac{1}{4} \times \frac{1}{2}[/tex] powered punch mix cups are required to make [tex]\frac{1}{4}[/tex] recipe.So,[tex]\frac{1}{8}[/tex] cups of powered punch mix cups are required to make [tex]\frac{1}{4}[/tex] recipe.