Point K is taken on a 28 cm segment AB. Find the lengths of segments AK and BK if AK is 6 times less than BK.

Let x be the proportionality coefficient, then: AK = x, ВK = 6x (since, according to the condition, AK is 6 times less than ВK, then ВK is 6 times more than AK).
AK + ВK = AB;
x + 6x = 28;
7x = 28;
x = 28/7;
x = 4 cm.
AK = x = 4 cm, ВK = 6x = 6 * 4 = 24 (cm).
Check: AK + ВK = 28;
4 + 24 = 28;
28 = 28.
Answer: AK = 4 cm, ВK = 24 cm.