A 12 cm segment AB is divided by a point C into segments AC and CB in a ratio of 3: 1. Find the length

A 12 cm segment AB is divided by a point C into segments AC and CB in a ratio of 3: 1. Find the length of the line segment AC and the length of the line segment CB.

To solve this example, we will use two conditional variables “X” and “Y”, through which we denote the lengths of the segments AC and CB, respectively.
Using the data from the example, create the following expressions:
1) X + Y = 12;
2) X / Y = 3/1.
Solving a system of two equations with two unknowns, we obtain X = 3Y.
Substituting X in the first equation, we have 3Y + Y = 12 or 4Y = 12 or Y = 12/4 = 3 cm.
Therefore, X = 3 x 3 = 9 cm.
Answer: segments AC and CB have lengths of 9 cm and 3 cm, respectively.