The length of the segment AB is 3. Point M is taken inside the segment. Find the length of the segment BM

The length of the segment AB is 3. Point M is taken inside the segment. Find the length of the segment BM if: a) AM = 2BM; c) 2AM = 3ВM; c) AM: BM = 1: 5.

AB = 3; ВM =?
The segment length AB consists of two parts:
AB = AM + BM.
Knowing this, we will find the ВM.
a) AM = 2BM;
2ВМ + ВМ = 3;
3BM = 3;
BM = 3: 3 = 1;

c) 2AM = 3ВM;
AM = 3 / 2BM;
3 / 2ВМ + ВМ = 3;
5 / 2ВМ = 3;
BM = 3: 5/2 = 6/5 = 1.2;

c) AM: BM = 1: 5;
AM = BM * 1: 5;
AM = 1 / 5ВM;
1 / 5ВM + VM = 3;
6 / 5ВM = 3;
BM = 3: 6/5 = 3 * 5: 6 = 15/6 = 5/2 = 2.5.