. 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.
Answers
Age of friend 1= x
Age of friend 2= y
Sum of they're ages = 20
Product of their ages four years ago= 48
Product of their ages now= 48+4
= 52
x+y= 20
xy= 48
Till this is where i got... I dont knos how it is later... I am sooo sorry, i tried my bsst
Let present age of one friend = x years
and present age of other Friend = y years
We have,
x + y = 20 ............( 1 )
Four years ago,
Friend's age = ( x - 4 ) years
Other Friend's age = ( y - 4 ) years
Now,
Product of their age = 48 [ Given ]
( x - 5 ) ( y - 4 ) = 48
➪ xy - 4x - 4y + 16 = 48
➪ xy - 4 ( x - y ) - 32 = 0
➪ xy - 4 ( 20 ) - 32 = 0 [ From ( 1 ) ]
➪ xy - 80 - 32 = 0
➪ xy = 112 ..............( 2 )
From ( 1 ) and ( 2 ) , we get
x ( 20 - x ) = 112
➪ x² - 20x + 112 = 0
D = b² - 4ac
➪ ( -20 )² - 4 × 1 × 112
➪ 400 - 448
➪ -48 < 0
As D < 0 , therefore, the equation has no real roots.
So, Situation is not possible.