Point C is located on a straight line between points A and B. The length of the segment CB is 3 cm longer than the length of the segment AC. Find the length of the segments AC and CB if the length of the segments AB is 33 cm.
Let the length of the AC segment be x cm, then the length of the BC segment is (x + 3) cm (if it is 3 cm more, then add 3 cm to the AC length). By the condition of the problem, it is known that the length of the segment AB is equal to the sum of the lengths of the segments into which it is divided by any point (we have this point C; AB = AC + BC), i.e. (x + (x + 3)) cm or 33 cm Let us compose the equation and solve it.
x + (x + 3) = 33;
x + x + 3 = 33;
2x + 3 = 33;
2x = 33 – 3;
2x = 30;
x = 30: 2;
x = 15 (cm) – length of the AC segment;
x + 3 = 15 + 3 = 18 (cm) – the length of the BC segment.
Answer. AC = 15 cm; BC = 18 cm.
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