A 1.5 meter segment was cut into parts that are proportional to the numbers 7 and 23. Find the lengths of these segments.

If the lengths of the segments are proportional to the numbers 7 and 23, then this means that the length of one segment is equal to 7 equal parts of the length, and the second segment is equal to 23 of the same parts.

Let the length of one part be x meters, then the length of one segment is 7 meters, and the length of the second segment is 23 meters. By the condition of the problem, it is known that the sum of the lengths of the segments is (7x + 23x) meters or 1.5 meters. Let’s make an equation and solve it.

7x + 23x = 1.5;

30x = 1.5;

x = 1.5: 30;

x = 0.05 (m) – the length of one part;

7x = 0.05 * 7 = 0.35 (m) – the length of one segment;

23x = 0.05 * 23 = 1.15 (m) – the length of the second segment.

Answer. 0.35 m, 1.15 m.