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The problem involves calculating the approximate change in demand based on a price elasticity of demand (E) and a price increase.

Given:
- Initial price $ P = 78 $ dollars
- Elasticity $ E(78) = 3.1 $
- Price increase $ \Delta P = 9 $ dollars

### Solution:
The formula to approximate the percentage change in demand based on elasticity is:

\[
\text{Percentage change in demand} = E \times \frac{\Delta P}{P} \times 100\%
\]

Substitute the values:
\[
= 3.1 \times \frac{9}{78} \times 100\%
\]

Calculating step-by-step:

1. $\frac{9}{78} \approx 0.1154$
2. $3.1 \times 0.1154 \approx 0.3577$
3. Multiply by 100 to get a percentage: $0.3577 \times 100 \approx 35.77\%$

Thus, the demand will **decrease by approximately 35.77%** when the price is increased by $9.

Would you like further details on this calculation?

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1. What is the concept of price elasticity of demand?
2. How does a price increase generally affect demand with high elasticity?
3. What are other methods to calculate elasticity-related changes?
4. Why is elasticity important in pricing strategy?
5. How would a decrease in price affect demand in this scenario?

**Tip:** Remember, elasticity greater than 1 (like 3.1) indicates high sensitivity to price changes.

Assume that the price of a pair of running shoes is $78 and E(78) = 3.1. If the price is increased by $9, then what is the approximate change in demand? Round your answer to the nearest hundredth of a percent.

Learn how to calculate the approximate change in demand for a pair of running shoes with an initial price of $78 and elasticity of 3.1. This example demonstrates the formula to determine demand change due to a $9 price increase.

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