Question

Sum of the present ages of two friends are 23 years five years ago product of their ages was 42. Find their ages 5 years hence. ​

Answer 1

Given :   sum of the present ages of two friends are 23 years

Let present age of one friend is x years

then present age of other friend is (23- x) years

Also given five years ago product of their ages was 42.

five year ago, age of one friend is (x - 5) years

and five year ago, age of other friend is (18 - x) years

thus,

(x - 5) x (18 - x) = 42

 

Apply distributive rule  (a+b) x (c+d) = ac + ad + bc + bd

23x - x² - 90 = 42

-x² + 23x - 132 = 0

 

Simplify for x by factorizing ,

Using middle term splitting method,

23x can be written as -11x and -12x

-x² + 11x + 12x - 132 = 0

Taking -x common from first two term and -12x common from last two terms, we have,

-x (x-11) + 12(x - 11) = 0

(x - 11) + (-x+12) = 0

 

Thus, x = 11 and  x = 12  

When x = 11 age of other friend will be 23 - 11 = 12  

when x = 12 age of other friend will be 23 - 12 = 11  

Thus, their ages 5 year hence will be 11 + 5 = 16 and 12 + 5 = 17

 

Thus, their ages 5 year hence will be 16 and 17 years.