Suppose a stock drops in value by 40% one week, then increases in value the next week by 75%. Is the value higher or lower than where it started?
The value of the stock is  than where it started.
If the value of the stock started at $100, then what is it worth now? 

Let's break down the problem:

1. **Initial drop of 40%:**
   - If the stock starts at $100 and drops by 40%, it loses 40% of its value.
   - The loss is:  
   \[
   40\% \text{ of } 100 = 0.40 \times 100 = 40
   \]
   - After the drop, the stock is worth:
   \[
   100 - 40 = 60
   \]

2. **Subsequent increase of 75%:**
   - After the drop, the stock is now worth $60.
   - A 75% increase on $60 is:
   \[
   75\% \text{ of } 60 = 0.75 \times 60 = 45
   \]
   - After the increase, the stock is now worth:
   \[
   60 + 45 = 105
   \]

Thus, the stock's value after these changes is **$105**, which is **higher** than where it started.

### Final Answer:
- The value of the stock is higher than where it started.
- If the stock started at $100, it is now worth **$105**.

Would you like further details or clarifications on any part of this?

Here are 5 follow-up questions related to this topic:
1. What happens if a stock drops by 50% and then increases by 50%? Will the value be the same?
2. How does the order of percentage changes affect the final value of a stock?
3. What is the formula for calculating percentage change over multiple periods?
4. How do you calculate the total percentage change from successive increases and decreases?
5. If a stock increases by 100% after dropping 50%, what will be its final value?

**Tip:** When a percentage decrease is followed by a percentage increase, the increase is always calculated on a smaller base, making it harder to fully recover from large drops.

Suppose a stock drops in value by 40% one week, then increases in value the next week by 75%. Is the value higher or lower than where it started? If the value of the stock started at $100, then what is it worth now?

Learn how to calculate the final value of a stock that drops by 40% and then increases by 75%. This problem covers essential percentage concepts, with step-by-step calculations, starting from an initial value of $100. Suitable for Grades 6-8.

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