Darrin and sharon are riding the merry-go-round with their son, aaron. sharon and aaron together are 32 years old; the sum of sharon’s and darrin’s ages is 54; and darrin’s age added to aaron’s equals 34 years. how many years difference is there between father and son?me asap (as soon as possible

Let the ages be s, a and d.  
Then s+a = 32, s + d = 54, and d+a = 34.
Here you have 3 equations in 3 unknowns, so you have enuf info to solve this problem.

Start with s+d=54 and subtract s+a=32.  We get d-a=54-32 = 22.

d - a = 22
d + a = 34  Combine these 2 equations:

2d = 56, d = 28.     If d-a=22, then 28-a=22, and a = 6.

Find s.  Since s+a=32, s+6=32, and s=26.

Sharon is 26 years old, Darrin is (34-6), or 28, and Aaron is 6 years old.

The diff between father's and son's ages is 28-6 = 22.

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !