Paul is six years older than Gary.

The sum of their ages is 30.

What are their ages?

Answer: Paul is 18 years old and Gary is 12 years old.

Step-by-step explanation:

Let x represent the age of Paul.

Paul is six years older than Gary. This means that Gary's age would be

x - 6

The sum of their ages is 30. This means that

x + x - 6 = 30

2x - 6 = 30

Adding 6 to the left hand side and the right hand side of the equation, it becomes

2x - 6 + 6 = 30 + 6

2x = 36

Dividing the left hand side and the right hand side of the equation by 2, it becomes

2x/2 = 36/2

x = 18

Therefore, Paul is 18 years old.

Gary is 18 - 6 = 12 years old.