To find out how many pounds of flour Eric should use for 1 cup of sugar, we can set up a proportion based on the recipe.
The recipe states that the ratio of flour to sugar is \( 2 \frac{1}{2} \) pounds of flour for every \( \frac{1}{4} \) cup of sugar.
First, we convert \( 2 \frac{1}{2} \) into an improper fraction:
\[ 2 \frac{1}{2} = \frac{5}{2} \text{ pounds of flour} \]
Next, we need to compare this with \( 1 \) cup of sugar. Since \( 1 \) cup is equal to \( 4 \times \frac{1}{4} \), we can set up the relationship like this:
\[ \text{If } \frac{1}{4} \text{ cup of sugar uses } \frac{5}{2} \text{ pounds of flour, then } 1 \text{ cup of sugar uses } x \text{ pounds of flour.} \]
Thus, our equation becomes:
\[ \frac{5}{2} \text{ pounds of flour} \cdot 4 = x \]
Calculating this gives:
\[ x = \frac{5}{2} \cdot 4 = \frac{5 \cdot 4}{2} = \frac{20}{2} = 10 \]
Therefore, Eric should use 10 pounds of flour for 1 cup of sugar.
The answer is \( \boxed{10} \).