Final answer:
The problem is a math word problem where the student is asked to find the ages of a mother and daughter based on two given equations related to their ages. By setting up algebraic equations, it is determined that the daughter is 10 years old and the mother is 15 years old.
Step-by-step explanation:
The problem presented is a classic age-related word problem in algebra. We are looking to find the present ages of a mother and her daughter given two conditions:
- The mother's age is 5 years less than twice the daughter's age.
- When the mother was the age the daughter is now, the product of their ages was 125.
Let the daughter's current age be d years, and the mother's current age be m years.
According to the first condition:
m = 2d - 5 ... (1)
For the second condition, when the mother was the age of the daughter now, the mother's age then was d. If we subtract the difference in their current ages (which is also the elapsed time since that moment) from the mother's current age, we have:
m - (m - d) = 125
Using the first equation to express m in terms of d, we can solve this as a quadratic equation to find the value of d. Once we have d, we can easily find m using equation (1).
After solving, we find that the daughter is 10 years old, and the mother is 15 years old as the present ages that satisfy both conditions.