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The problem presented involves direct proportionality. Here's how we can solve it:

Erin took 12 quizzes in 3 weeks, and we need to find out how many quizzes she will take after 5 weeks if the relationship is directly proportional.

### Step-by-Step Solution:
1. Set up a proportion based on the idea that the number of quizzes Erin takes is proportional to the number of weeks:
   \[
   \frac{12 \text{ quizzes}}{3 \text{ weeks}} = \frac{x \text{ quizzes}}{5 \text{ weeks}}
   \]
   where \(x\) is the number of quizzes Erin will take in 5 weeks.

2. Cross-multiply to solve for \(x\):
   \[
   12 \times 5 = 3 \times x
   \]
   \[
   60 = 3x
   \]

3. Divide both sides by 3:
   \[
   x = \frac{60}{3} = 20
   \]

So, Erin will take **20 quizzes** after 5 weeks.

Would you like more details on this solution or further clarifications?

Here are 5 related questions to explore further:
1. What is a direct proportion, and how does it differ from an inverse proportion?
2. How would the problem change if the relationship were inversely proportional?
3. What is the formula for setting up a proportion when solving real-world problems?
4. How do you solve proportions using cross-multiplication?
5. How can you check if your solution to a proportionality problem is correct?

### Tip:
When working with proportional relationships, always ensure the units on both sides of the equation match (e.g., quizzes per week).

Erin took a total of 12 quizzes over the course of 3 weeks. After attending 5 weeks of school this quarter, how many quizzes will Erin have taken in total? Assume the relationship is directly proportional.

Solve a word problem involving direct proportionality: Erin took 12 quizzes in 3 weeks. Find out how many quizzes Erin will take in 5 weeks using cross-multiplication. This problem is perfect for Grades 6-8, focusing on algebra and proportion concepts.

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