A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages?

A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages?

Let the woman's age be w.
Let the mother's age be m.

We're given two equations:

1. w = m/2
2. m + w = 75

Substitute equation (1) into equation (2) for w:
m + m/2 = 75

To solve for m, we type this equation into our search engine and we get:
m = 50

To solve for w, we plug m = 50 into equation (1):
w = 50/2
w = 25