Answer:
Tom will need [tex]\dfrac{5}{4}[/tex] gallons of fruit drink.
Step-by-step explanation:
Hint- This question can be solved by unitary method.
Tom has a recipe for punch that calls for [tex]\dfrac{1}{2}[/tex] gallon of fruit drink.
i.e for 1 batch of the punch Tom needs [tex]\dfrac{1}{2}[/tex] gallon of fruit drink.
For [tex]\dfrac{5}{2}[/tex] batch of the punch Tom needs [tex]\dfrac{1}{2}\times \dfrac{5}{2}=\dfrac{5}{4}[/tex] gallons of fruit drink.
Therefore, Tom will need [tex]\dfrac{5}{4}[/tex] gallons of fruit drink.