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To find the price of the evening dress in 2021, given that it was $172 in 2001, we can use the inflation proportion based on the Consumer Price Index for All Urban Consumers (CPI-U) values provided in the table. The formula for adjusting the price using CPI is:

\[
\text{Price in 2021} = \text{Price in 2001} \times \frac{\text{CPI in 2021}}{\text{CPI in 2001}}
\]

### Given Data:
- **Price in 2001**: $172
- **CPI in 2001**: 177.1
- **CPI in 2021**: 271.0

### Calculation:

\[
\text{Price in 2021} = 172 \times \frac{271.0}{177.1}
\]

1. First, calculate the CPI ratio:
   \[
   \frac{271.0}{177.1} \approx 1.5304
   \]

2. Then, multiply the 2001 price by this ratio:
   \[
   172 \times 1.5304 \approx 263.23
   \]

### Answer:
The estimated price of the evening dress in 2021 is **$263** (rounded to the nearest dollar).

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Would you like more details or have any questions?

### Related Questions:
1. How would you calculate the price of an item for any given year using CPI?
2. What does the Consumer Price Index (CPI) measure, and why is it used to adjust prices?
3. If the CPI continues to rise, what will happen to the future prices of goods purchased today?
4. How would you calculate the inflation rate over multiple years using CPI values?
5. How do you determine the percentage increase in the cost of an item using CPI?

### Tip:
To find future or past prices using CPI, always set up a proportion based on the index values from the years of interest.

Assume that the price for the evening dress, purchased in 2001 for $172, increased at the average annual rate shown in the table. Use the inflation proportion to find the missing price in the last column of the chart, representing the price in 2021.

Learn how to calculate the 2021 price of an item originally purchased in 2001 for $172, using Consumer Price Index (CPI) values for inflation adjustment. This solution covers the formula for adjusting prices with CPI and demonstrates proportional reasoning. Suitable for high school students and those studying inflation effects.

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