The wholesale cost of a birdcage is $55. The original markup was 46% based on selling price. Find the final sale price (in $) after the following series of price changes: a markdown of 14% and a markup of 13%. (Round each intermediate selling price to the nearest cent.) 

To find the final sale price of the birdcage, we will follow these steps:

### Step 1: Find the original selling price based on the wholesale cost and the markup percentage.

The formula for markup based on the selling price is:

\[
\text{Markup based on selling price} = \frac{\text{Selling price} - \text{Wholesale cost}}{\text{Selling price}}
\]

Given that the markup is 46%, this means:

\[
\frac{\text{Selling price} - 55}{\text{Selling price}} = 0.46
\]

Let $ x $ represent the selling price. Rearranging the equation:

\[
x - 55 = 0.46x
\]
\[
x - 0.46x = 55
\]
\[
0.54x = 55
\]
\[
x = \frac{55}{0.54} \approx 101.85
\]

So, the original selling price is **$101.85**.

---

### Step 2: Apply the 14% markdown to the original selling price.

The formula for markdown is:

\[
\text{New price} = \text{Original price} \times (1 - \text{Markdown percentage})
\]

Here, the markdown is 14%, so:

\[
\text{New price} = 101.85 \times (1 - 0.14) = 101.85 \times 0.86 \approx 87.59
\]

After the markdown, the new price is **$87.59**.

---

### Step 3: Apply the 13% markup to the new price.

The formula for markup is:

\[
\text{New price} = \text{Current price} \times (1 + \text{Markup percentage})
\]

Here, the markup is 13%, so:

\[
\text{New price} = 87.59 \times (1 + 0.13) = 87.59 \times 1.13 \approx 98.98
\]

After the markup, the final sale price is **$98.98**.

---

### Final Answer: The final sale price of the birdcage is **$98.98**.

Would you like further details on any of these steps?

---

**Related Questions:**
1. What would the selling price be if the initial markup was 50%?
2. How would the final price change if the markdown was 10% instead of 14%?
3. What would be the final price if there was an additional 5% discount after the last markup?
4. How is the final price affected if both the markdown and markup were 20%?
5. What would happen if the markup was based on the wholesale price instead of the selling price?

**Tip:** When dealing with percentages, always clarify whether it's based on the selling price or cost price to avoid confusion.

The wholesale cost of a birdcage is $55. The original markup was 46% based on selling price. Find the final sale price (in $) after the following series of price changes: a markdown of 14% and a markup of 13%. (Round each intermediate selling price to the nearest cent.)

Learn how to calculate the final sale price of a birdcage with a wholesale cost of $55, including a 46% markup, 14% markdown, and 13% markup. This step-by-step solution explains the key concepts of percentage-based price changes. Suitable for Grades 8-10.

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