To determine how many avocados Desiree needs for 1 cup of lime juice, we can set up a proportion based on the recipe.
The recipe states that for every 4 avocados, 14 cups of lime juice are used. We can represent this relationship as:
\[ \frac{14 \text{ cups lime juice}}{4 \text{ avocados}} = \frac{1 \text{ cup lime juice}}{x \text{ avocados}} \]
Next, we can cross-multiply to solve for \( x \):
\[ 14 \times x = 1 \times 4 \]
This simplifies to:
\[ 14x = 4 \]
Now, divide both sides by 14:
\[ x = \frac{4}{14} \]
Simplifying this fraction gives:
\[ x = \frac{2}{7} \]
Thus, Desiree needs \(\frac{2}{7}\) of an avocado for 1 cup of lime juice. Since avocados cannot be easily obtained in fractions for cooking purposes, she may need to round to the nearest whole number depending on her preference or the context of the recipe. In practice, she would likely use 1 avocado.
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