Question

in 1983, a cast-iron pan cost \\$28.35. today, a cast-iron pan costs \\$52.95. if the cpi is 166, what is the percent relation of the actual price of a cast-iron pan to the expected price?
a. the actual price is 11.1\\% lower than the expected price.
b. the actual price is 20.8\\% lower than the expected price.
c. the actual price is 31.5\\% higher than the expected price.
d. the actual price is 12.5\\% higher than the expected price.

Explanation:

Calculate the expected price today

Using the Consumer Price Index and Inflation Adjustment knowledge points

$$ \text{Expected Price} = \text{Price in 1983} \times \frac{\text{CPI}}{100} $$

$$ \text{Expected Price} = 28.35 \times \frac{166}{100} = 28.35 \times 1.66 = 47.061 $$

Compare actual price to expected price

Using the Percentage Increase knowledge point

$$ \text{Percent Difference} = \frac{\text{Actual Price} - \text{Expected Price}}{\text{Expected Price}} \times 100\% $$

$$ \text{Percent Difference} = \frac{52.95 - 47.061}{47.061} \times 100\% = \frac{5.889}{47.061} \times 100\% \approx 12.51\% $$

Since the result is positive, the actual price is approximately \(12.5\%\) higher than the expected price.

Answer:

• a. The actual price is 11.1% lower than the expected price.
• b. The actual price is 20.8% lower than the expected price.
• c. The actual price is 31.5% higher than the expected price.
• d. The actual price is 12.5% higher than the expected price. (Correct answer)