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The problem states that the average weekly allowance of children varies **directly** with their grade level. This indicates a direct variation relationship, which can be written mathematically as:

\[
A = k \cdot G
\]

Where:
- \( A \) is the weekly allowance,
- \( G \) is the grade level,
- \( k \) is the constant of proportionality.

We are given:
- For a 9th-grade student, the allowance is \( 9.66 \) dollars per week.
- We need to find the allowance for a 4th-grade student.

### Step 1: Find the constant of proportionality \( k \)
Using the known values for the 9th-grade student:
\[
9.66 = k \cdot 9
\]
Solving for \( k \):
\[
k = \frac{9.66}{9} = 1.0733
\]

### Step 2: Use \( k \) to find the allowance for a 4th-grade student
Now, using the formula \( A = k \cdot G \) for the 4th-grade student:
\[
A = 1.0733 \cdot 4
\]
\[
A = 4.2932 \text{ dollars per week}
\]

Therefore, the average weekly allowance for a 4th-grade student is approximately **4.29 dollars**.

Would you like further clarification or additional details on this problem?

### Related Questions:
1. How would the allowance change if the relationship were inverse instead of direct?
2. How can we find the allowance for a student in any other grade using this model?
3. What if the allowance for a 6th grader is 6.5 dollars per week, does the direct variation still hold?
4. How would this problem change if we added inflation or cost-of-living adjustments over time?
5. Can you model the allowance for multiple students using different grade levels?

**Tip**: In direct variation, always look for a constant relationship between two quantities, so once you know the constant, you can predict other values easily.

According to Fidelity Investment Vision Magazine, the average weekly allowance of children varies directly as their grade level. In a recent year, the average allowance of a 9th-grade student was 9.66 dollars per week. What was the average weekly allowance of a 4th-grade student?

Learn how to calculate the average weekly allowance for students using direct variation. This example uses a 9th-grade student's allowance of 9.66 dollars to find the weekly allowance for a 4th grader, applying key algebraic concepts. Suitable for Grades 6-9 students.

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