Joyce wants to go to the zoo with her friend over spring break. You can pay $45 to get into the zoo each time, or join a membership for $50 and then only pay $20 each visit to the zoo. How many times will Joyce need to visit the zoo to justify the expense of the membership fee?

To determine how many times Joyce needs to visit the zoo to justify the membership fee, we can set up an equation comparing the cost of paying per visit versus the membership fee plus the per visit cost after joining.

1. **Cost without membership:**
Each visit costs $45.
So, for \( x \) visits, the total cost is \( 45x \).

2. **Cost with membership:**
The membership fee is $50, and each visit after joining costs $20.
So, for \( x \) visits, the total cost is \( 50 + 20x \).

We want to find the value of \( x \) where the costs are equal, i.e., when:
\[ 45x = 50 + 20x \]

Next, we'll solve for \( x \):

1. Subtract \( 20x \) from both sides:
\[ 45x - 20x = 50 \]
\[ 25x = 50 \]

2. Divide both sides by 25:
\[ x = \frac{50}{25} \]
\[ x = 2 \]

So, Joyce needs to visit the zoo **2 times** to justify the expense of the membership fee.

The answer is **2**.