Geometry - Find measurements?

Question

Could anyone explain to me how these types of problema are done?

Find the value of the variable and BC if B is between A and C

AB = 4x, BC = 5x, AB = 16

AB = 9a, BC = 12a, AC = 42

AB = 5n +5, BC = 2n, AC = 54

Answer 1

Imagine a line with the endpoints A and C and a point somewhere between them called B.

Then, we know that the length of AB + length of BC = length of AC, or

AB + BC = AC

1) 4x + 5x = 16

9x = 16

x = 16/9

BC = 5x = 5*16/9 = 80/9

2) 9a + 12a + 42

21a = 42

a = 2

BC = 12a = 12*2 = 24

3) (5n + 5) + 2n = 54

7n + 5 = 54

7n = 49

n = 7

BC = 2n = 2*7 =14