Matt is five years older than twice his cousin andy’s age. the sum of their ages is less than 35. what is the greatest age that andy could be?

Since there are two unknowns, Matt's age and Andy's age, we need to formulate two algebraic equations in order to solve the system. The first independent equation that we could form, is the relation ship of their ages. Suppose we let Matt's age be equal to x. Andy's age will be denoted as y. Then,

x = 5 + 2y

The second independent equation would be the sum of their ages:
x + y ≤ 35
As you can observe, I used an inequality with the symbol ≤ which means less than or equal to. It means that their sum could be less than or equal to 35. So, the equation is

x + y ≤ 35

Solving the equation, 
5 + 2y + y ≤ 35
3y ≤ 35-5
3y ≤ 30
y ≤ 10

Thus, Andy's greatest age could be 10 years old.