To find the amount of flour needed for a triple recipe when a double recipe calls for 5 cups of flour, we first calculate the amount of flour needed for a single recipe.
If a double recipe (which is 2 servings) calls for 5 cups of flour, then a single recipe (which is 1 serving) would call for: \[ \text{Flour for single recipe} = \frac{5 \text{ cups}}{2} = 2.5 \text{ cups}. \]
Now, for a triple recipe (which is 3 servings), we need: \[ \text{Flour for triple recipe} = 3 \times 2.5 \text{ cups} = 7.5 \text{ cups}. \]
Now we need to find the correct proportion to express \(f\) (the amount of flour needed for the triple recipe) in relation to the double recipe.
Among the options given, we want to find the correct proportion that yields \(f = 7.5\).
Let's analyze the proportions provided:
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\( \frac{2}{5} = \frac{f}{3} \): This implies \(f = \frac{2}{5} \cdot 3 = 1.2 \neq 7.5\)
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\( \frac{5}{2} = \frac{f}{3} \): This implies \(f = \frac{5}{2} \cdot 3 = 7.5\) (This is a match)
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\( \frac{3}{2} = \frac{5}{f} \): This implies \(3f = 10 \Rightarrow f = \frac{10}{3} \approx 3.33 \neq 7.5\)
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\( \frac{2}{3} = \frac{f}{5} \): This implies \(2f = 15 \Rightarrow f = 7.5\) (This is a match)
So, the correct proportions that could be used to find the amount of flour for a triple recipe are:
- \( \frac{5}{2} = \frac{f}{3} \)
- \( \frac{2}{3} = \frac{f}{5} \)
Thus, options 2 and 4 can be used to find the amount of flour for a triple recipe, giving us \(f = 7.5\) cups.
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