Question 996950
Call the mother's age now, x.  The daughter's age is y.
Thus x + y = 47, and x = 47 - y.
In five years,
x + 5 = 6 + 2(y + 5)  or
x + 5 = 6 + 2y + 10
x + 5 = 2y + 16
x = 2y + 11
Substituting in, we get
47 - y = 2y + 11
36 = 3y
y = 12
x = 35