To determine how many avocados Desiree needs for 1 cup of lime juice, we can set up a proportion based on the original recipe.
The recipe calls for 14 cup of lime juice for every 4 avocados. First, let's express that relationship mathematically:
\[ \frac{14 \text{ cup lime juice}}{4 \text{ avocados}} = \frac{1 \text{ cup lime juice}}{x \text{ avocados}} \]
Now we can cross-multiply to solve for \(x\):
\[ 14x = 4 \times 1 \]
\[ 14x = 4 \]
Now, divide both sides by 14 to solve for \(x\):
\[ x = \frac{4}{14} = \frac{2}{7} \]
So, Desiree needs \(\frac{2}{7}\) of an avocado for every 1 cup of lime juice, which means she will need to use \(\frac{2}{7}\) avocados.
However, it seems inconsistent since in practice she would need a whole number of avocados. Hence, if she's making guacamole for a party, she would likely need to round this to the nearest whole number for a practical answer. In this case, she could use 1-2 avocados depending on the recipe's requirements for taste and texture.
In summary, mathematically, she needs \(\frac{2}{7}\) of an avocado for 1 cup, but practically, she should use approximately 2 avocados (she could also adjust lime juice to match the number of avocados if needed).
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