Question

in 1983, a winter hat cost $12.95. today, a winter hat costs $24.50. if the cpi is 219, what is the percent relation of the actual price of a winter hat to the expected price?
a. the actual price is 39.3% higher than the expected price.
b. the actual price is 15.8% higher than the expected price.
c. the actual price is 13.6% lower than the expected price.
d. the actual price is 29.8% lower than the expected price.
please select the best answer from the choices provided

Explanation:

Step1: Calculate expected price

The formula to calculate the expected price using CPI is $Expected\ Price = \text{1983 Price} \times \frac{\text{CPI}}{100}$.
Given 1983 price is $\$12.95$ and CPI is 219.
So, $Expected\ Price = 12.95\times\frac{219}{100}=12.95\times2.19 = 28.3605$ (approx $\$28.36$).

Step2: Calculate percent difference

The actual price is $\$24.50$. Since actual price ($24.50$) is less than expected price ($28.36$), we calculate the percent decrease.
The formula for percent decrease is $\text{Percent Difference}=\frac{\text{Expected Price}-\text{Actual Price}}{\text{Expected Price}}\times100$.
Substitute the values: $\frac{28.36 - 24.50}{28.36}\times100=\frac{3.86}{28.36}\times100\approx13.6\%$.

Answer:

c. The actual price is 13.6% lower than the expected price.