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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.
Solution
Let the age of one friend be x years.
Then the age of the other friend will be (20 - x) years.
4 years ago,
Age of 1st friend = (x - 4) years
Age of 2nd friend = (20 - x - 4) = (16 - x) years
According to the question,
(x - 4) (16 - x) = 48
16x - x2 - 64 + 4x = 48
- x2 + 20x - 112 = 0
x2 - 20x + 112 = 0
Comparing this equation with ax2 + bx + c = 0, we get
a = 1, b = -20 and c = 112
Discriminant = b2 - 4ac = (-20)2 - 4 × 112
= 400 - 448
= -48
b2 - 4ac < 0
Therefore, there will be no real solution possible for the equations. Such type of condition doesn't exist.
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