The recipe calls for \( \frac{1}{4} \) cup of lime juice for every 4 avocados.
To find how many avocados are needed for 1 cup of lime juice, we can set up a proportion:
\[ \frac{1/4 \text{ cup lime juice}}{4 \text{ avocados}} = \frac{1 \text{ cup lime juice}}{x \text{ avocados}} \]
To solve for \( x \), we cross-multiply:
\[ 1/4 \cdot x = 1 \cdot 4 \] \[ \frac{x}{4} = 4 \]
Now, multiply both sides by 4:
\[ x = 4 \cdot 4 \] \[ x = 16 \]
Therefore, Desiree needs 16 avocados for 1 cup of lime juice.