We are tasked with finding the final sale price of a birdcage, given a series of price changes. Here's the step-by-step approach:

1. Step 1: Calculate the original selling price (before price changes)
   The wholesale cost of the birdcage is $55, and the original markup is 44% based on the selling price. Let $p$ represent the original selling price.

   The formula for markup based on selling price is: $\text{Wholesale cost} = p - 0.44p = 0.56p$ Solving for $p$: $55 = 0.56p$ $p = \frac{55}{0.56} = 98.21$ So, the original selling price is $p = 98.21$.

2. Step 2: Apply an 18% markdown
   The birdcage is marked down by 18%, so the new price after the markdown is calculated as: $\text{New price after markdown} = 98.21 \times (1 - 0.18) = 98.21 \times 0.82 = 80.53$ After rounding, the price after the markdown is $80.53$.

3. Step 3: Apply an 11% markup
   Now, we apply an 11% markup to the new price. The price after the markup is calculated as: $\text{New price after markup} = 80.53 \times (1 + 0.11) = 80.53 \times 1.11 = 89.39$ After rounding, the final selling price is $89.39$.

Final Sale Price:

The final sale price after the series of price changes is $89.39.

Would you like more details or have any questions?
Here are 5 related questions you might want to consider:

1. How does the original markup calculation differ when based on cost instead of selling price?
2. What happens if the markdown is greater than the markup?
3. How can you apply these concepts to pricing strategies in retail?
4. How would the problem change if intermediate rounding wasn’t allowed?
5. How does inflation or deflation impact pricing strategies like this?

Tip: Always double-check the base you're using for percentage calculations (selling price vs. cost). It changes the markup or markdown amounts significantly!