Final answer:
To make enough pancakes for 31 people, each eating 2 pancakes, the mother will need approximately 13.78 cups of flour, based on her recipe.
Step-by-step explanation:
The student's question involves determining how much flour is needed for making pancakes for 31 people where each person eats 2 pancakes. The mother's recipe makes 9 pancakes with 2 cups of flour. To solve this, we calculate the total number of pancakes needed, which is 31 people × 2 pancakes/person = 62 pancakes. Since the recipe makes 9 pancakes from 2 cups of flour, we can use a proportion to find out how many cups are needed for 62 pancakes.
Set up the ratio as follows: 9 pancakes/2 cups = 62 pancakes/x cups. Cross-multiply to find x: 9x = 2 × 62, which simplifies to 9x = 124. Solving for x gives us x = 124 / 9, which is approximately 13.78 cups of flour. Therefore, the mother will need approximately 13.78 cups of flour to make enough pancakes for the extended family.