Three years ago a father was four times as old as his daughter is now. The product of their present ages is 430. Calculate the present ages of the daughter and the father.
Let F be the current age of the father.
Let D be the current age of the daughter.
Then,
F * D = 430
Also,
(F - 3) = D * 4 (The father's age, 3 yrs ago, was 4 times the daughter's current age)
F = 4D + 3
Substituting for F = 4D + 3 into FD = 430,
(4D + 3)D = 430
4D^2 + 3D - 430 = 0
(4D + 43)(D - 10) = 0
D = -43/4 (ignore this solution for age since it is negative)
D = 10
So, daughter's age is 10, Father's age is 43