Mother's age: x
Sara's age: x/2 (half of her mother's age)
Sum of their ages = 75
Equation:
x + x/2 = 75
(2)x + (2)x/2 = 75 (2)
2x + x = 150
3x = 150
3x/3 = 150/3
x = 50
Mother's age: x = 50 years old
Sara's age: x/2 = 50/2 = 25 years old (half of her mother's age)
Sum of their ages:
50 + 25 = 75
ANSWER: Sara is 25 years old.