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From 1980 to 2000, the consumer price index (CPI) increased from 122.5 to 181. If a pound of tomatoes cost [tex]\$0.75[/tex] in 1980 and the price of tomatoes increased at the same rate as the CPI from 1980 to 2000, approximately how much did a pound of tomatoes cost in 2000?

Answer :

To find out how much a pound of tomatoes would cost in 2000 if the price increased at the same rate as the Consumer Price Index (CPI), we can follow these steps:

1. Understand the CPI Change:
- In 1980, the CPI was 122.5.
- In 2000, the CPI increased to 181.

2. Calculate the Rate of Increase:
- To determine how much the CPI increased, we calculate the ratio of the CPI in 2000 to the CPI in 1980.
- This ratio can be calculated as [tex]\( \frac{181}{122.5} \approx 1.4775\)[/tex].

3. Apply the Rate of Increase to the Tomato Price:
- The initial price of a pound of tomatoes in 1980 was [tex]$0.75.
- Since the price increased at the same rate as the CPI, we multiply this initial price by the ratio we calculated.
- Calculate the 2000 price as \( 0.75 \times 1.4775 \approx 1.108\).

Therefore, if the price of a pound of tomatoes increased at the same rate as the CPI did from 1980 to 2000, the price in 2000 would be approximately $[/tex]1.11.

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