Felicia can purchase at most 5 pairs of shoes to stay within her budget.
To find the number of pairs of shoes that Felicia can purchase and stay within her budget, we can set up an inequality.
Let's assume Felicia can buy x pairs of shoes.
The average cost of one pair of shoes is $85, so she would spend 85x dollars on the shoes.
Since she gets a $20 discount, the total cost would be 85x - 20 dollars.
The inequality can be written as:
85x - 20 ≤ 405
To solve for x, we can add 20 to both sides of the inequality:
85x ≤ 425
Dividing both sides by 85, we get:
x ≤ 5
Therefore, Felicia can purchase at most 5 pairs of shoes to stay within her budget. We can represent this on a graph by shading the region to the left of the point (5, 0) on the x-axis since she can only buy whole pairs of shoes.