To determine how many pounds of flour Eric should use for 1 cup of sugar, we first need to understand the relationship between the amount of flour and sugar given in the recipe.
The recipe states that 2 1/2 pounds of flour is used for every 1/4 cup of sugar. We can express this relationship mathematically.
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Convert 2 1/2 pounds to a fraction: \[ 2 \frac{1}{2} = \frac{5}{2} \text{ pounds of flour} \]
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Determine how many 1/4 cups are in 1 cup: Since there are 4 quarters in 1 cup: \[ 1 \text{ cup} = 4 \times \frac{1}{4} \text{ cup} \]
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Set up a proportion based on the given relationship: If 2 1/2 pounds (or \( \frac{5}{2} \) pounds) of flour is used for 1/4 cup of sugar, then for 1 cup of sugar (which is 4 times 1/4 cup), the amount of flour needed would be: \[ \text{Flour for 1 cup} = 4 \times \frac{5}{2} \text{ pounds} \]
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Calculate the total amount of flour: \[ \text{Flour for 1 cup} = 4 \cdot \frac{5}{2} = \frac{20}{2} = 10 \text{ pounds of flour} \]
Therefore, Eric should use 10 pounds of flour for 1 cup of sugar.