Question

4. Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years Four years ago, the product of their ages
m years was 48
stan
IS​

Answer 1

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Is the following situation possible? If so,determine their present ages.

The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

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Let the present age of one friend be x years.

Then, the present age of other friend = (20-x) years.

Four years ago , one's friend age was (x-4) years.

According to the Question,

$(x - 4)(16 - x) = 48$

$\implies16x - {x}^{2} - 64 + 4x = 48$

$\implies - {x}^{2} - 20x - 64 - 118 = 0$

$\implies - {x}^{2} - 20x + 112 = 0$

Here, a = 1 , b = -20 & c = 112

Discriminant ,

D = $b^2$-4ac

= $(-20)^2-4×1×112$

= 400-448 = -48<0

$\therefore$ No real roots exists for x.

Hence, the Given equation is not possible.