2. Pat is six years older than twice his Cousin Zach's age. The sum of their ages is less than 36.

What is the greatest age that Zach could be?

Let denote Pat's age with P and Zach's age with Z.

We know the following facts:

1. Pat is six years older than twice his Cousin Zach’s age. We can rewrite this statement as:

P=2*Z+6

2. The sum of their ages is less than 36.

P+Z<36

In order to find the greatest age that Zach could be we should find for which Z

P+Z=35 (the first whole number smaller than 36)

P=35-Z

35-Z=2*Z+6

35-6=3Z

29=3Z

Z=29/3

Z=9

P = Pat

C = Cousin Zach

2C + 6 = P

2C + 6 - 6 = P - 6

2C = P - 6

2C/2 = P - 6/2

C = P - 3

C + 3 = P

so (C + 3) + P < 36

(C + 3 - 3) + P < 36 - 3

C + P < 33

Can you see what I am doing?