Five years hence , the age of Jacob will bethree times that of his son. Five years ago Jacob's age was seven times that of his son. What are their present ages

Solution  :

Let the present age of Jacob be x

Let the present age of his son be y

After five years 

Jacob will be ( x + 5 )

His son will be ( y + 5 )

According to the first statement 

x + 5 = 3 ( y + 5 )

x + 5 = 3y + 15

x - 3y = 15 - 5

                            x - 3y = 10.         Equation ( 1 )

Five years ago

Jacob will be ( x - 5 )

His son's  age will be ( y - 5)

According to the second statement 

x - 5 = 7 ( y - 5 )

x - 5 = 7y - 35

x - 7y = -35 + 5

x - 7y = - 30.           Equation ( 2 )

Take both equations and solve

x - 3y = 10

x - 7y = -30

                                     -   +        +                  ( change  signs) 

...................

     +4y = + 40

          y = 10

Substitute y =10 in equation  ( 1 )

x - 3y = 10

x - 3 ( 10 ) = 10

x -  30 = 10

x = 10 +30

x = 40

Hence  age of Jacob is 40 years

And his son's age is 10 years.