To determine how many pounds of flour Eric should use for 1 cup of sugar based on the recipe, we start with the given ratio of flour to sugar.
The recipe states that 2 1/2 pounds of flour is used for every 1/4 cup of sugar.
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First, let's convert 2 1/2 pounds to an improper fraction: \[ 2 \frac{1}{2} = \frac{5}{2} \text{ pounds of flour} \]
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Next, we need to figure out how many 1/4 cups fit into 1 cup: \[ 1 \text{ cup} = 4 \times \frac{1}{4} \text{ cups} \]
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Since 1 cup is equivalent to 4 times the amount of sugar in the recipe, we can now find how many pounds of flour are needed for 1 cup of sugar: \[ \text{Flour for } 1 \text{ cup of sugar} = 4 \times \left(\frac{5}{2} , \text{pounds of flour}\right) \]
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Now, multiply: \[ 4 \times \frac{5}{2} = \frac{20}{2} = 10 \text{ pounds of flour} \]
So, Eric should use 10 pounds of flour for 1 cup of sugar.
The answer is: 10 pounds of flour.