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?

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?

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