Question

The difference of the present ages of two sister in 5 yrs

After 4yrs if the product of their age becomes 104. fine
their present age-​

Answer 1

4 and 9

Explanation:

let their ages be x and x - 5, then in 4 years their ages will be

x + 4 and x - 5 + 4 = x - 1 , and the product is 104, thus

(x + 4)(x - 1) = 104 ← expand factors on left using FOIL

x² + 3x - 4 = 104 ( subtract 104 from both sides )

x² + 3x - 108 = 0 ← in standard form

(x + 12)(x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 12 = 0 ⇒ x = - 12

x - 9 = 0 ⇒ x = 9

However, x > 0 ⇒ x = 9

Thus

Their present ages are 9 and 9 - 5 = 4