in 1983, a winter hat cost $12.95. today, a winter hat costs $24.50. if the cpi is 219, what is the percent…

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?\na. the actual price is 39.3% higher than the expected price.\nb. the actual price is 15.8% higher than the expected price.\nc. the actual price is 13.6% lower than the expected price.\nd. the actual price is 29.8% lower than the expected price.

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?\na. the actual price is 39.3% higher than the expected price.\nb. the actual price is 15.8% higher than the expected price.\nc. the actual price is 13.6% lower than the expected price.\nd. the actual price is 29.8% lower than the expected price.

Answer

Explanation:

Step1: Calcular el precio esperado

El CPI en 1983 es 100. Usamos la fórmula $\text{Precio esperado}=\text{Precio en 1983}\times\frac{\text{CPI actual}}{\text{CPI en 1983}}$. Entonces, $\text{Precio esperado}=12.95\times\frac{219}{100}=12.95\times2.19 = 28.3605$.

Step2: Calcular la diferencia porcentual

Usamos la fórmula $\text{Diferencia porcentual}=\frac{\text{Precio actual}-\text{Precio esperado}}{\text{Precio esperado}}\times 100%$. Sustituyendo valores: $\frac{24.50 - 28.3605}{28.3605}\times100%=\frac{- 3.8605}{28.3605}\times100%\approx - 13.6%$. Un valor negativo significa que el precio actual es menor que el precio esperado.

Answer:

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