The number of hours a particular student spends doing homework is inversely proportional to the number of hours they spend scrolling through TikToks. If this student spends 5 hours on homework on a night where they spend 5 hours on TikTok, how many hours will they spend on homework the next night when they spend 4 hours on TikTok? (Hint: Use proportional reasoning!)

To solve this problem, we will use the concept of inverse proportionality. The formula for inverse proportionality between two variables \( x \) and \( y \) is:

\[
x \cdot y = k
\]

where \( k \) is a constant.

Let:
- \( x_1 = 5 \) hours (time spent on homework when TikTok time is \( y_1 = 5 \) hours),
- \( y_2 = 4 \) hours (time spent on TikTok the next night),
- \( x_2 \) is the time spent on homework the next night, which we are solving for.

From the inverse proportionality relationship, we know:

\[
x_1 \cdot y_1 = x_2 \cdot y_2
\]

Substitute the known values:

\[
5 \cdot 5 = x_2 \cdot 4
\]

Now solve for \( x_2 \):

\[
25 = 4x_2
\]

\[
x_2 = \frac{25}{4} = 6.25 \text{ hours}
\]

So, the student will spend **6.25 hours on homework** the next night when they spend 4 hours on TikTok.

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:
1. What does it mean for two quantities to be inversely proportional?
2. How do you solve a proportion problem with direct proportionality?
3. If the student spends 3 hours on TikTok, how much time will they spend on homework?
4. Can you explain why inverse proportionality results in less time on homework when more time is spent on TikTok?
5. What are some real-life examples of inverse proportionality?

**Tip**: Inverse proportionality means when one variable increases, the other decreases at the same rate!

This problem demonstrates how to apply inverse proportionality to find out how much time a student spends on homework when their TikTok time changes. Learn how to solve for unknowns using the inverse proportionality formula. Suitable for Grades 6-8 students.

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