We are given that:

- \( \frac{AD}{BD} = \frac{3}{4} \)
- \( AC = 15 \)
- We are asked to find \( AE \).

Assuming that point \( E \) lies on line segment \( AC \) and point \( D \) divides \( AC \) into two segments, such that \( AD = 3x \) and \( BD = 4x \), let's break it down:

### Step 1: Find the Total Length of \( AB \)
Since \( AD + BD = AB \), we can express \( AB \) in terms of \( x \):
\[
AD = 3x \quad \text{and} \quad BD = 4x
\]
Thus,
\[
AB = AD + BD = 3x + 4x = 7x
\]

### Step 2: Relating \( AC \) to \( AB \)
Now, since \( AB \) is the whole length and \( AC = 15 \), we need to determine where point \( E \) lies relative to these distances.

Would you like more information about the location of \( E \) on \( AC \), or should we assume a midpoint scenario? 

Here are some follow-up questions to clarify:
1. Is point \( E \) specified as a particular division point on \( AC \)?
2. Should \( E \) be located using ratios or other geometric relationships?
3. Do you need additional clarification on how \( AD \) and \( BD \) divide \( AB \)?
4. Should we consider any particular type of triangle or line configuration here?
5. Would you like a visual breakdown?

**Tip:** Always clarify the relationship between points when solving geometric problems to ensure accurate interpretation.

Learn how to solve a geometric problem where AD/BD = 3/4 and AC = 15. This problem involves ratios, proportions, and segment division. Follow the step-by-step breakdown suitable for students in Grades 8-10.

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