Multiple choice

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 $48$.

  1. Not Possible

  2. Yes , 8 and 6

  3. Yes  ,12 and 4

  4. none
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let ages be x and 20-x. Four years ago: (x-4)(20-x-4) = 48. (x-4)(16-x) = 48. 16x - x^2 - 64 + 4x = 48. -x^2 + 20x - 112 = 0. Discriminant = 20^2 - 4(-1)(-112) = 400 - 448 = -48. Since the discriminant is negative, no real ages exist.

AI explanation

Let the present ages of the two friends be x and 20 minus x. Four years ago, their ages were x minus 4 and 16 minus x, and their product is given as 48. This gives the quadratic equation x minus 4 times 16 minus x equals 48, which simplifies to x squared minus 20x plus 112 equals 0. The discriminant of this quadratic is 400 minus 448, which equals negative 48. Since the discriminant is negative, there are no real roots, making the situation not possible.

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