To determine how many pounds of flour Eric should use for 1 cup of sugar, we can set up a proportion based on the information given in the recipe:
- The recipe calls for \(2 \frac{1}{2}\) pounds of flour for \( \frac{1}{4}\) cup of sugar.
First, convert \(2 \frac{1}{2}\) to an improper fraction:
\[ 2 \frac{1}{2} = \frac{5}{2} \text{ pounds of flour} \]
Now, we can set up the ratio of flour to sugar:
\[ \frac{5/2 \text{ pounds of flour}}{1/4 \text{ cup of sugar}} \]
Now we want to find out how much flour is needed for 1 cup of sugar. Since 1 cup is 4 times \( \frac{1}{4} \) cup, we can multiply the amount of flour by 4 as well:
\[ \text{Flour for } 1 \text{ cup of sugar} = \left(\frac{5}{2} \text{ pounds of flour}\right) \times 4 \]
Calculating this gives:
\[ \text{Flour for } 1 \text{ cup of sugar} = \frac{5}{2} \times 4 = \frac{20}{2} = 10 \text{ pounds of flour} \]
Therefore, Eric should use 10 pounds of flour for 1 cup of sugar. The correct answer is:
10