SOLUTION: Cary is 7 years older than Dan. In 3 years the sum of their ages will be 83. Find the age of each man now.

You are given that  "In 3 years the sum of their ages will be 83."

It means that NOW the sum of their ages is 83-3-3 = 77.


So, you have these two equations

C = D +  7,   (1)
C + D = 77.   (2)


In equation (2), replace "C"  by (D+7), based on (1). You will get

(D+7) + D = 77  ====>  2D + 7 = 77  ====>  2D = 77-7 = 70  ====>  D =  = 35.


Thus Dan is 35 years old.


Then Cary is 35+7 = 42 years old.