The points x, y, z for which 3XY = 5YZ are located on the straight line. Find the length of the line segment XY if XZ = 24 cm.

1. Let’s denote the length of the segment XY through x.

2. Determine the length of the segment YZ:

3/5 * x = 0.6x.

3. The length of the segment XZ is equal to the sum of the lengths of the segments into which it is divided by the point Y, that is, XZ = XY + YZ.

Let’s compose and solve the equation:

0.6x + x = 24;

1.6 x = 24;

x = 24: 1.6;

x = 15.

4. The length of the XY segment is 15 cm.

Answer: The length of the XY segment is 15 cm.