Answer :
To solve this problem, we need to calculate the Consumer Price Index (CPI) for the year 2009, using the prices from the provided table and a base year (2005 in this case).
Here is how you can calculate the CPI:
1. Identify the Prices for Each Year:
- 2005 (Base Year):
- Price of Hot Dogs: [tex]$2.00
- Price of Baseballs: $[/tex]5.00
- Price of Bottles of Beer: [tex]$2.00
- 2009:
- Price of Hot Dogs: $[/tex]10.00
- Price of Baseballs: [tex]$10.00
- Price of Bottles of Beer: $[/tex]4.00
2. Calculate the Average Price for Each Year:
- Average Price in 2005:
[tex]\[
\text{Average Price}_{2005} = \frac{\$2.00 + \$5.00 + \$2.00}{3} = \frac{\$9.00}{3} = \$3.00
\][/tex]
- Average Price in 2009:
[tex]\[
\text{Average Price}_{2009} = \frac{\$10.00 + \$10.00 + \$4.00}{3} = \frac{\$24.00}{3} = \$8.00
\][/tex]
3. Calculate the Consumer Price Index for 2009:
The Consumer Price Index is calculated by taking the average price of the items in 2009, dividing by the average price in the base year (2005), and then multiplying by 100 to convert it to a percentage:
[tex]\[
\text{CPI}_{2009} = \left(\frac{\text{Average Price}_{2009}}{\text{Average Price}_{2005}}\right) \times 100
\][/tex]
Plugging in the values we calculated:
[tex]\[
\text{CPI}_{2009} = \left(\frac{\$8.00}{\$3.00}\right) \times 100 = 266.67
\][/tex]
So, the Consumer Price Index for the year 2009 is approximately 266.67, which suggests significant inflation from the base year 2005. However, none of the options provided in the multiple-choice answers match this result exactly. You might want to double-check the calculations or consider potential rounding differences. Based on the understanding and results, 223.5 is the closest reasonable assumption from the provided options, though it is important to clarify the calculation basis further if possible.
Here is how you can calculate the CPI:
1. Identify the Prices for Each Year:
- 2005 (Base Year):
- Price of Hot Dogs: [tex]$2.00
- Price of Baseballs: $[/tex]5.00
- Price of Bottles of Beer: [tex]$2.00
- 2009:
- Price of Hot Dogs: $[/tex]10.00
- Price of Baseballs: [tex]$10.00
- Price of Bottles of Beer: $[/tex]4.00
2. Calculate the Average Price for Each Year:
- Average Price in 2005:
[tex]\[
\text{Average Price}_{2005} = \frac{\$2.00 + \$5.00 + \$2.00}{3} = \frac{\$9.00}{3} = \$3.00
\][/tex]
- Average Price in 2009:
[tex]\[
\text{Average Price}_{2009} = \frac{\$10.00 + \$10.00 + \$4.00}{3} = \frac{\$24.00}{3} = \$8.00
\][/tex]
3. Calculate the Consumer Price Index for 2009:
The Consumer Price Index is calculated by taking the average price of the items in 2009, dividing by the average price in the base year (2005), and then multiplying by 100 to convert it to a percentage:
[tex]\[
\text{CPI}_{2009} = \left(\frac{\text{Average Price}_{2009}}{\text{Average Price}_{2005}}\right) \times 100
\][/tex]
Plugging in the values we calculated:
[tex]\[
\text{CPI}_{2009} = \left(\frac{\$8.00}{\$3.00}\right) \times 100 = 266.67
\][/tex]
So, the Consumer Price Index for the year 2009 is approximately 266.67, which suggests significant inflation from the base year 2005. However, none of the options provided in the multiple-choice answers match this result exactly. You might want to double-check the calculations or consider potential rounding differences. Based on the understanding and results, 223.5 is the closest reasonable assumption from the provided options, though it is important to clarify the calculation basis further if possible.
