The sum of the present ages of a father and his daughter is 80 years. Eight years ago, the father's age was seven times the age of his daughter. Eight years from now, what will be the daughter's age?

Explanation

Let the present age of the father be F and the present age of the daughter be D. 1. Given: The sum of their ages is 80 years: 2. Given: Eight years ago, the father's age was seven times the age of the daughter: Step 2: Solve the Equations From the first equation: F = 80 - D Substitute this value of F in the second equation: (80 - D) - 8 = 7(D - 8) Simplify: 72 - D = 7D - 56 Add D and 56 to both sides: 128 = 8D Divide by 8: D = 16 Now, use the first equation to find F: F = 80 - 16 = 64 Step 3: Calculate the Daughter's Age Eight Years from Now The daughter's current age D is 16. Eight years from now, her age will be: D + 8 = 16 + 8 = 24 Final Answer The daughter's age eight years from now will be 24 years.