Labels:
-- Mary's age = D (for 'daughter')
-- Mom's age = M (for 'mom')
The problem says 2 things:
D + M = 67
and
3D + 7 = M .
Let's subtract 'M' from each side of the first one: D = 67 - M
Now we can plug that into the second one, in place of 'D'.
3D + 7 = M
3(67 - M) + 7 = M .
Clear the parentheses on the left side. I assume you know how to do that.
201 - 3M + 7 = M
Add 3m to each side:
201 + 7 = 4M
208 = 4M
Divide each side by 4 :
52 = Mom's age
Daughter's age = 67 - Mom's age = 67 - 52 = 15