a tank was 1/2 full of water. After 420 gallons had been taken out, it was 1/8 full. Find the capacity of the tank?

Let V be full volume.

We are told: V/2 -420 = V/8

Subtract V/8 from both sides: V/2 - V/8 - 420 = 0

Add 420 to both sides: V/2 - V/8 = 420

Simplify the left hand side: 3V/8 = 420

Multiply both sides by 8/3: V = 420*8/3

Simplify: V = 140*8 or V = 1120 gallons