Question

a father is five times as old as his son. three years ago the product of their ages was 329. find them

Answer 1

Answer:

sons age = 10

father age = 50

Step-by-step explanation:

let the present age of son be x

present age of father will be 5x

age of son three years ago x - 3

age of father three years ago 5x - 3

$(x - 3)(5x - 3) = 329 \\ 5 {x}^{2} - 3x - 15x + 9 = 329 \\ 5{x}^{2} - 18x + 9 = 329 \\ 5{x}^{2} - 18x + 9 - 329 = 0 \\ 5{x}^{2} - 18x - 320 = 0 \\ 5 {x}^{2} - 50x + 32x - 320 = 0 \\ 5x(x - 10) + 32(x - 10) = 0 \\ (x - 10)(5x + 32) = 0 \\ x - 10 = 0 \: \: \: \: 5x + 32 = 0 \\ x = 10 \: \: \: \: x = - \frac{32}{5}$

we take the positive value of x = 10

age of son = x =10

age of father = 5x = 5 × 10 = 50

hope you get your answer