A recipe uses 2 cups of beans to make 9 cups of soup. How many gallons of this soup can be made using 6 quarts of beans.

We know that:

1 quart = 4 cups

1 cup = 0.0625 gallons

And given is:

2 cups = 9 cups of soup

so,

1 cup = 4.5 cups of soup

going back to the top and using that equation:

1 quart = 4 cups

1/4 quarts = 1 cup

so,

1/4 quarts = 0.0625 gallons

to make it 6 quarts:

(1/4) x 24 = 24 x 0.0625

6 quarts = 1.5 gallons