How much water is needed to prepare 333 portions of beef stew if the recipe calls for 6 gallons of water per 100 portions?

To determine how much water is needed for 333 portions of beef stew when the recipe specifies 6 gallons of water for every 100 portions, we can set up a proportion based on the provided information.

First, find out how many gallons are required for each portion. If 6 gallons are needed for 100 portions, then for 1 portion, the amount of water required would be:

[ \text{Water per portion} = \frac{6 \text{ gallons}}{100 \text{ portions}} = 0.06 \text{ gallons per portion} ]

Next, multiply the gallons per portion by the total number of portions (333):

[ \text{Total water required} = 333 \text{ portions} \times 0.06 \text{ gallons per portion} = 19.98 \text{ gallons} ]

This calculation indicates that approximately 20 gallons of water is necessary. To express this more precisely, we can convert 0.98 gallons into quarts (since there are 4 quarts in a gallon):

[ 0.98 \text{ gallons} = 0.98 \times 4 = 3.92 \text{ quarts