To determine how many avocados Desiree needs if she is using 1 cup of lime juice, we can set up a proportion based on the recipe.
The recipe states that 1/4 cup of lime juice is used for every 4 avocados.
First, let's calculate how many times 1/4 cup fits into 1 cup:
\[ 1 \text{ cup} \div \frac{1}{4} \text{ cup} = 1 \times \frac{4}{1} = 4 \]
This means 1 cup of lime juice is equivalent to 4 times the amount of lime juice from the recipe.
Since the recipe calls for 4 avocados for every 1/4 cup of lime juice, we can multiply the number of avocados by 4:
\[ 4 \text{ avocados} \times 4 = 16 \text{ avocados} \]
Therefore, Desiree needs 16 avocados to make guacamole with 1 cup of lime juice.