In the diagram, ab: bc is 3: 4 and ac: 42 find bc

From the diagram:
AB + BC = AC
we know that AC = 42, therefore:
AB + BC = 42 ..............> equation I

We know that the ratio AB:BC is 3:4. This means that:
AB/BC = 3/4
4AB = 3BC
AB = (3/4) BC ...............> equation II

Substitute by equation II in equation I to get BC as follows:
(3/4) BC + BC = 42
1.75 BC = 42
BC = 24

Substitute with the value of BC in equation II to get AB as follows:
AB = (3/4) * 24 = 18

Sometimes life is like a tunnel. you can’t always see the light at the end of the tunnel, but if you keep moving, you will come to a better place