Is the following situation.
if
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
present age
Answers
Answer:
Situation is not possible
Step-by-step explanation:
Let the present ages of two friends be 'x' and 'y' years
Sum of present ages of two friends = 20 years
⇒ x + y = 20
⇒ y = 20 - x
Age of one of the friend four years ago = ( x - 4 ) years
Age of the other friend four years ago = ( y - 4 ) years = ( 20 - x - 4 ) = ( 16 - x ) years
Product of their ages four years ago = 48 years
⇒ ( x - 4 )( 16 - x ) = 48
⇒ x( 16 - x ) - 4( 16 - x ) = 48
⇒ 16x - x² - 64 + 4x = 48
⇒ - x² + 20x - 64 - 48 = 0
⇒ - x² + 20x - 112 = 0
⇒ x² - 20x + 112 = 0
Comparing the above equation with ax² + bx + c = 0 we get
- a = 1
- b = - 20
- c = 112
Discriminant = D = b² - 4ac
= ( - 20 )² - 4( 1 )( 112 )
= 400 - 448
= - 48
Since D < 0, the equation has no real roots
Therefore the situation is not possible.
Let’s say, the age of one friend be x years.
Then, the age of the other friend will be (20 – x) years.
Four years ago,
Age of First friend = (x – 4) years
Age of Second friend = (20 – x – 4) = (16 – x) years
As per the given question, we can write,
(x – 4) (16 – x) = 48
16x – x2 – 64 + 4x = 48
– x2 + 20x – 112 = 0
x2 – 20x + 112 = 0
Comparing the 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. Hence, condition doesn’t exist.