Percent Increase Problems – Introductory Statistics Guidance

Q1. In 2025, a concert venue shows a 20% increase in the average ticket sales since 2023. If average ticket sales were 2400 in 2023, what is the average ticket sales in 2025?

Background

Topic: Percent Increase

This question tests your understanding of how to calculate a new value after a percent increase is applied to an original value. This is a common application in statistics for interpreting changes over time.

Key Terms and Formulas

• Percent Increase: The amount by which a value grows, expressed as a percentage of the original value.

• Original Value: The starting value before the increase (here, ticket sales in 2023).

• New Value Formula:

$\text{New Value} = \text{Original Value} \times (1 + \text{Percent Increase})$

Where percent increase is written as a decimal (e.g., 20% = 0.20).

Step-by-Step Guidance

1. Identify the original value: Ticket sales in 2023 = 2400.

2. Convert the percent increase to a decimal: 20% = 0.20.

3. Set up the formula: $\text{New Value} = 2400 \times (1 + 0.20)$

4. Calculate the value inside the parentheses first: $1 + 0.20$

5. Multiply the original value by the result from the previous step to find the new value.

Try solving on your own before revealing the answer!

Final Answer: 2880

$\text{New Value} = 2400 \times (1 + 0.20) = 2400 \times 1.20 = 2880$

The average ticket sales in 2025 is 2880, reflecting a 20% increase from 2023.

Q2. Another venue of similar size also shows an increase of 30% in average ticket sales over the same time period. If the average ticket sales in 2025 are 3900, what was the average ticket sales in 2023?

Background

Topic: Percent Increase (Reverse Calculation)

This question tests your ability to work backwards from a final value after a percent increase to find the original value. This is useful for understanding how changes affect starting values.

Key Terms and Formulas

• Percent Increase: The percentage by which the original value increased.

• Final Value: The value after the increase (here, ticket sales in 2025).

• Original Value Formula:

$\text{Original Value} = \frac{\text{Final Value}}{1 + \text{Percent Increase}}$

Where percent increase is written as a decimal (e.g., 30% = 0.30).

Step-by-Step Guidance

1. Identify the final value: Ticket sales in 2025 = 3900.

2. Convert the percent increase to a decimal: 30% = 0.30.

3. Set up the formula: $\text{Original Value} = \frac{3900}{1 + 0.30}$

4. Calculate the denominator: $1 + 0.30$

5. Divide the final value by the result from the previous step to find the original value.

Try solving on your own before revealing the answer!

Final Answer: 3000

$\text{Original Value} = \frac{3900}{1 + 0.30} = \frac{3900}{1.30} = 3000$

The average ticket sales in 2023 was 3000, before the 30% increase.