Points M, N, K move on one straight line. MK = 28 cm, the NK segment is 3 times smaller than the MN segment.

Points M, N, K move on one straight line. MK = 28 cm, the NK segment is 3 times smaller than the MN segment. Find the segment MN. How many solutions does the problem have?

Let us denote the length of the segment NK by x.

Determine the length of the segment MN:

3 * x = 3x.

1st way:

Let point N lie between points M and K, then the length of the segment MK is equal to the sum of the lengths of the segments MN and NK.

Let’s compose and solve the equation:

3x + x = 28;

4x = 28;

x = 28: 4;

x = 6.

The length of the segment NK is x = 6 cm.

How long is the segment MN?

3 * x = 3 * 6 = 18 cm.

Answer: the length of the segment MN is 18 cm.

2nd way:

Let the point K lie between the points M and N, then the length of the segment MK is equal to the difference between the lengths of the segments MN and NK.

Let’s compose and solve the equation:

3x – x = 28;

2x = 28;

x = 28: 2;

x = 14.

The length of the segment NK is 14 cm.

How long is the segment MN?

3 * x = 3 * 14 = 42 cm.

Answer: the length of the segment MN is 42 cm.