Question

A recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water and 3/4 quart of grape juice. How much of each ingredient would you need to make 100 quarts of punch? How much of each ingredient would you need to make 100 quarts of punch?

A. 100 quarts sparkling water & 50 quarts grape juice

B. 70 quarts sparkling water & 30 quarts grape juice

C. 50 quarts sparkling water & 50 quarts grape juice

D. 66 2/3 quarts sparkling water & 33 1/3 quarts grape juice

Answer 1

D. 66 2/3 quarts sparkling water & 33 1/3 quarts grape juice

Explanation:

You want the quantities of ingredients required to make 100 quarts of punch that uses 1 1/2 quarts of sparkling water for each 3/4 quart of grape juice.

Ingredients

The fraction of the total that is sparkling water is ...

sparkling water / (sparkling water +grape juice)

= (1 1/2 qt)/(1 1/2 +3/4 qt) = (3/2)/(3/2 +3/4)

= (6/4)/(9/4) = 6/9 = 2/3

Then the amount of 100 quarts that is sparkling water is ...

(2/3) × 100 qt = 66 2/3 qt

The remaining quantity is grape juice:

100 qt -66 2/3 qt = 33 1/3 qt

The ingredient amounts are ...

• 66 2/3 quarts sparkling water
• 33 1/3 quarts grape juice