Question

a recipe for sparkling grape juice calls for 1.5 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

Answer 1

Answer:

$33\dfrac{1}{3}\text{ quarts of grape juice}\\ \\66\dfrac{2}{3}\text{ quarts of sparkling water}$

Step-by-step explanation:

A recipe for sparkling grape juice calls for 1.5 quarts of sparkling water and 3/4 quart of grape juice.

The ratio of sparkling water to grape juice is

$1.5\div \dfrac{3}{4}=\dfrac{3}{2}\div \dfrac{3}{4}=\dfrac{6}{4}\div \dfrac{3}{4}=6\div 3=2\div 1$

So, to make 100 quarts of punch you need x quarts of grape juice and 2x quarts of sparkling water.

Hence,

$x+2x=100\\ \\3x=100\\ \\x=\dfrac{100}{3}=33\dfrac{1}{3}\text{ quarts of grape juice}\\ \\2x=66\dfrac{2}{3}\text{ quarts of sparkling water}$