The problem presents a proportional relationship where \(6\) is to \(15\) as \(36\) is to an unknown value \(x\). We can set this up as a proportion:

\[
\frac{6}{15} = \frac{36}{x}
\]

### Step-by-Step Solution:
1. **Set up the proportion**:
   \[
   \frac{6}{15} = \frac{36}{x}
   \]

2. **Cross-multiply to solve for \(x\)**:
   \[
   6 \times x = 15 \times 36
   \]

3. **Calculate the right side**:
   \[
   6x = 540
   \]

4. **Divide both sides by 6 to solve for \(x\)**:
   \[
   x = \frac{540}{6} = 90
   \]

So, \(36\) is to **90**.

Would you like more details or have any questions?

### Related Questions:
1. What if the relationship were \(6\) to \(12\) as \(36\) to \(x\)? What would \(x\) be?
2. Can you explain why cross-multiplication works in proportions?
3. What is the ratio of 15 to 6, and how does it compare to the ratio of 90 to 36?
4. If the numbers in the proportion were doubled, would the relationship still hold?
5. How can you check if two ratios are equivalent?
6. What if the second number was 24 instead of 15? How would that change the answer?
7. What if the first number was 9 instead of 6?
8. Can this type of proportional reasoning be applied to more complex scenarios?

### Tip:
Always check the proportionality by simplifying ratios. If two ratios are equal when simplified, the proportion holds true!

Learn how to solve the proportional relationship problem: 6 is to 15 as 36 is to x. Follow a step-by-step solution with cross-multiplication and division to find the value of x. Suitable for students in Grades 6-8.

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