Arecipe 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