Devin learned to play a total of 6 pieces over the course of 3 weeks of piano lessons. In all, how many weeks of piano lessons will Devin need before he will be able to play a total of 46 pieces? Assume the relationship is directly proportional.


To find out how many weeks of piano lessons Devin will need to learn 46 pieces, given that the relationship between the number of pieces learned and the time spent learning is directly proportional, we can set up a proportion.

Given:
- 6 pieces in 3 weeks.
- We need to find the number of weeks, \( x \), required to learn 46 pieces.

The proportion can be set up as follows:

\[
\frac{6 \text{ pieces}}{3 \text{ weeks}} = \frac{46 \text{ pieces}}{x \text{ weeks}}
\]

Now, solve for \( x \):

\[
x = \frac{46 \text{ pieces} \times 3 \text{ weeks}}{6 \text{ pieces}} = \frac{138 \text{ weeks} \cdot \text{ pieces}}{6 \text{ pieces}} = 23 \text{ weeks}
\]

So, Devin will need **23 weeks** of piano lessons to learn 46 pieces.

Would you like more details on the calculation or have any questions? 

Here are some related questions you might find interesting:
1. How many pieces can Devin learn in 10 weeks?
2. If Devin wanted to learn 30 pieces, how many weeks would it take?
3. How many pieces could Devin learn in 1 week?
4. How long would it take Devin to learn 100 pieces?
5. How many pieces can Devin learn in 15 weeks?
6. How much time is required to learn 20 pieces?
7. What would happen if Devin's learning rate increased over time?
8. Can you express the number of pieces learned as a function of time?

**Tip:** When working with directly proportional relationships, setting up a proportion is a straightforward way to solve for unknown quantities.

Find out how many weeks of piano lessons Devin needs to learn 46 pieces using a proportional relationship. Given that he learned 6 pieces in 3 weeks, this problem involves setting up a proportion and solving for the unknown weeks. Ideal for students in Grades 5-7.

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