Mrs. Smythe is twice as old as her daughter Samantha. Ten years ago the sum of their ages was 46 years. How old is Mrs. Smythe?

Mrs. Smythe = x

Daughter = y

x = 2y

(x - 10) + (y - 10) = 46

x - 10 + y - 10 = 46

x + y - 20 = 46

x + y = 66

Put 2y in for x

2y + y = 66

3y = 66

y = 66/3

y = 22

The daughter is 22

The mother = 44