To justify the expense of the membership fee, Joyce will need to visit the zoo enough times so that the total cost of individual visits (paying $45 each time) exceeds the cost of joining the membership ($50) plus the reduced price of each visit ($20).
Let's set up an equation to solve for the number of visits needed:
45 * x > 50 + 20 * x
Where x represents the number of visits.
Now, let's solve for x:
45x > 50 + 20x
25x > 50
x > 50/25
x > 2
Therefore, Joyce will need to visit the zoo more than 2 times to justify the expense of the membership fee.
Answer: 3 visits