Question

The sum if the ages of a father and his son is 45 years. Fiver years ago the product of their ages was 124

Answer 1

let x be age of father
let y be age. of son
now
$x + y = 45 \\ five \: years \: ago \\ (x - 5)(y - 5) = 124 \\ xy - 5x - 5y + 25 = 124 \\ xy - 5x - 5y = 99 \\ xy - 5(x + y) = 99 \\ xy - 5(45) = 99 \\ xy - 225 = 99 \\ xy = 324 \\ x = 324 \div y \\ put \: this \: value \: in \: first \: equation \\ (324 \div y) + y = 45 \\ 324 + {y}^{2} = 45y \\ {y}^{2} - 45y + 324 = 0 \\ {y}^{2} - (36 + 9)y + 324 = 0 \\ y = 36 \: or \: 9$
The age of father is 36 and age of son is 9.
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