Suppose that you hear on the news that inflation was 4.7 percent over the last 12 months. If today the Consumer Price Index (CPI) equals 266.8, what was the CPI equal to a year ago? Round to one decimal point.

To find the Consumer Price Index (CPI) from a year ago, we can use the formula that relates the current CPI, the inflation rate, and the CPI from a year ago:

\[
\text{CPI}_{\text{previous}} = \frac{\text{CPI}_{\text{current}}}{1 + \frac{\text{inflation rate}}{100}}
\]

Given:
- \(\text{CPI}_{\text{current}} = 266.8\)
- \(\text{inflation rate} = 4.7\%\)

Now, we can plug in the values:

\[
\text{CPI}_{\text{previous}} = \frac{266.8}{1 + \frac{4.7}{100}}
\]

\[
\text{CPI}_{\text{previous}} = \frac{266.8}{1.047}
\]

\[
\text{CPI}_{\text{previous}} \approx 254.8
\]

Thus, the CPI a year ago was approximately 254.8.

Would you like more details or have any questions? 

Here are five related questions:
1. How would the calculation change if the inflation rate was negative?
2. What does a rising CPI indicate about the economy?
3. How is the CPI used to measure cost-of-living adjustments?
4. What are some limitations of using the CPI as a measure of inflation?
5. How do different countries calculate their version of the CPI?

**Tip:** When calculating past values given a percentage change, remember to adjust for the change's direction (increase or decrease) in the formula.

Learn how to calculate the Consumer Price Index (CPI) from a year ago given a 4.7% inflation rate and a current CPI of 266.8. This problem involves percentage calculations and inflation formulas, making it suitable for high school students in Grades 9-12.

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