Question

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.

Answer 1

Answer:

No, the given situation is not possible.

Step-by-step explanation:

Let the present age of one friend be x years.

and present age of another friend be y years.

• First condition states that the sum of the ages of two friends is 20 years, i.e.;

               x + y = 20

               y = 20 - x ------------ [Equation 1]

• Second condition states that four years ago, the product of their ages in years was 48, i.e.;

               (x - 4) * (y - 4) = 48

               (x - 4) * (20 - x - 4) = 48

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

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

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

Now, using completing the squares method to find the value of x;

                    $x = \frac{-b \pm \sqrt{D} }{2a}$  where, a = 1 , b = -20 and c = 112

Firstly we will calculate $\sqrt{D}$ = $\sqrt{(-20)^{2}-(4*1*112) }$ = $\sqrt{-48}$

Since, the value inside the root can't be negative which means we can't find the present ages of two friend with the given situation.

Answer 2

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