High School

Here is Fred's basket of purchases in 2021:

- Pizzas: 20
- Beer: 50
- Gas: 30

The prices of these three items in 2021 are:

- Pizzas: $8
- Beer: $3
- Gas: $3.50

In 2022, the prices change to:

- Pizzas: $10
- Beer: $2
- Gas: $4.00

1. How much does Fred spend on his purchases in 2021?

2. How much does Fred spend on his purchases in 2022?

3. Create an index number for both years with 2021 being the base year. What is the index number representing the prices of 2021?

4. What is the index number representing prices in 2022?

5. What was the inflation rate from 2021 to 2022?

Answer :

1. Fred spends $290 on his purchases in 2021.

2. Fred spends $290 on his purchases in 2022.

3. The index number representing the prices of 2021 is 100.

4. The index number representing prices in 2022 is 112.5.

5. The inflation rate from 2021 to 2022 is 12.5%.

1. Fred spends $20 × $8 (pizzas) + $50 × $3 (beer) + $30 × (-$3.50) (gas) = $160 + $150 + (-$105) = $290.

2. The prices change, but Fred's purchases remain the same, so he spends the same amount as in 2021: $290.

3. The index number for 2021 is the base year, so it is set to 100.

4. To calculate the index number for 2022, we use the formula: (Total expenditure in 2022 / Total expenditure in 2021) × 100. Thus, (290 / 290) × 100 = 112.5.

5. The inflation rate is the percentage change in the index number from 2021 to 2022. It can be calculated as ((Index number in 2022 - Index number in 2021) / Index number in 2021) × 100. Therefore, ((112.5 - 100) / 100) × 100 = 12.5%.

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