Question 1004072
Call Joey's and his mother's age NOW, j and m.
From the facts we have
j + m = 46   (or j = 46 - m)
and
j + 4 = (1/2)(m + 4) - 3
Now substitute for j in the second equation and we get
46 - m + 4 = (1/2)(m + 4) - 3
50 - m = (1/2)m + 2 - 3
50 - m = (1/2)m - 1
Collect like terms and solve
51 = (3/2)m
m = 34 years old
j = 12 years old (46-34)