Final answer:
Direct variation in recipes means that the amount of an ingredient, like flour, changes proportionally with the number of servings. Scaling a recipe is mathematically straightforward: you multiply the original amount by the scaling factor, which is the ratio of the desired number of servings to the original number of servings.
Step-by-step explanation:
When preparing food for different numbers of servings, the amount of ingredients used, including flour, varies directly with the number of servings. This means that if you increase the number of servings, you proportionally increase the amount of ingredients. For instance, if a recipe calls for 1 cup of flour for 8 pancakes, and you want to make 24 pancakes, which is three times the original amount, you would need triple the amount of flour, hence 3 cups. This principle of scaling the amount of ingredients is similar to stoichiometric relationships in chemistry, where quantities of reactants and products are in fixed ratios.
Let's use a practical example. For two dozen pancakes, a recipe that uses 1 egg per 8 pancakes would need 3 eggs in total. This is due to the direct variation of servings and ingredients which can be represented with a simple mathematical relationship:
1 egg / 8 pancakes = x eggs / 24 pancakes
To find x, simply multiply both sides by 24 pancakes to get x = 24/8, which simplifies to 3 eggs. With larger events, such as preparing food for a party with 100 guests, where you'd need 375 milliliters of soup per person, you'd calculate the total amount needed by multiplying the serving size by the number of guests: 100 guests * 375 milliliters each = 37,500 milliliters, or 37.5 liters of soup.