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 $Expected\ price = \text{1983 price} \times \frac{\text{Current CPI}}{\text{1983 CPI}}$. Assuming 1983 CPI is 100 (base year), so $Expected\ price = 12.95\times\frac{219}{100}=12.95\times2.19 = 28.3605$.

Step2: Calculate percent difference

First, find the difference between actual price ($24.50$) and expected price ($28.3605$): $24.50 - 28.3605=- 3.8605$. Then, calculate the percent difference: $\frac{-3.8605}{28.3605}\times100\approx - 13.6\%$. The negative sign means the actual price is lower than expected.

Answer:

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