Final answer:
Using the information provided and setting up an equation, we found that there were initially 12 birds at the feeder before they were startled and flew away or moved to different locations.
Step-by-step explanation:
The question asks us to calculate how many birds were at the feeder initially, by using the given information that one-fourth of the birds flew away, two went to another feeder, three flew to a tree, and four remained at the feeder.
Let's denote the initial number of birds by x. One-fourth of the birds flying away means that ¼x birds are left. Therefore, the number of birds that remained is x - ¼x. But according to the scenario, 2 birds went to another feeder, 3 went to a tree, and 4 remained at the feeder. So we can write the equation: x - ¼x = 2 + 3 + 4. Simplifying the left side gives us ¾ x = 9. To find x, we multiply both sides of the equation by ⅔ (which is the reciprocal of ¾) to get x = 12.
So, initially, there were 12 birds at the feeder.