Question 927138
Let Carl's age = C
Let Lyn's age = L

Carl is 3 years older than Lyn
C = L + 3  ...eqn. (1)

In five years,
Carl's age = C + 5
Lyn's age = L + 5
The sum of their ages is 67
(C + 5) + (L + 5) = 67
C + 5 + L + 5 = 67
C + L + 10 = 67
C + L = 57   ...eqn. (2)

Subst. (L + 3) for C in eqn. (2)
L + 3 + L = 57
2L = 54
L = 27

Subst. 27 for L in eqn. (1)
C = 27 + 3 
C = 30

Carl is 30 years old; Lyn is 27 years old