https://file.aiquickdraw.com/mathbot/file/17258892715048xp3j674.jpg

In the problem provided, \( Y \) is a point between \( X \) and \( Z \), and the segments \( XY \), \( YZ \), and \( XZ \) are given as multiples of \( b \) and a specific value, respectively. We have the relationships:

- \( XY = 6b \)
- \( YZ = 8b \)
- \( XZ = 175 \)

Given that \( XZ \) is the entire distance from \( X \) to \( Z \), and \( Y \) is between \( X \) and \( Z \), the equation \( XZ = XY + YZ \) should hold. Substituting the given values:

\[ 175 = 6b + 8b \]

Let's solve this equation to find the value of \( b \) and then use it to find \( YZ \).The value of \( b \) is \( \frac{25}{2} \) or 12.5, and the length of segment \( YZ \) is 100.

If you have any further questions or need more details, feel free to ask! Here are some related questions you might consider:

1. How does changing the value of \( XZ \) affect the values of \( b \) and \( YZ \)?
2. What would be the length of \( XY \) based on the calculated value of \( b \)?
3. If the ratio of \( XY \) to \( YZ \) changes, how would that impact the value of \( b \)?
4. What is the significance of \( b \) in problems involving segment lengths?
5. Can you create a similar problem using different values and ratios for segment lengths?

**Tip:** When faced with problems involving segments of lines, setting up an equation based on the total length can simplify finding individual segment lengths.

Find the value of b and YZ if Y is between X and Z, XY = 6b, YZ = 8b, and XZ = 175.

This problem involves solving linear equations with segment addition, where XY = 6b, YZ = 8b, and the total distance XZ = 175. Learn to find the values of b and segment YZ with a detailed solution, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation