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.

Given:

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

To do:

We have to find their present ages.

Solution:

Let the present age of one of the friends be $x$ years.

This implies, the present age of the other friend$=20-x$ years.

The age of the first friend four years ago$=x-4$ years.

The age of the second friend four years ago$=20-x-4=16-x$ years.

According to the question,

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

$16x-x^2-64+4x=48$

$x^2-16x-4x+48+64=0$

$x^2-20x+112=0$

Comparing the above equation with the standard form of a quadratic equation $ax^2+bx+c=0$,

$a=1, b=-20$ and $c=112$

The discriminant of the standard form of a quadratic equation $ax^2+bx+c=0$ is $D=b^2-4ac$.

Therefore,

$D=(-20)^2-4(1)(112)$

$D=400-448$

$D=-48<0$

$D<0$, this implies, there are no real roots for the given equation.

Hence, the given situation is not possible.

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Updated on: 10-Oct-2022

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