In four years time a mother will be three times as old as her son. Four years ago she was five times as old as her son. Find their present ages

Question

In four years time a mother will be three times as old as her son. Four years ago she was five times as old as her son. Find their present ages

Answer 1

m = Mother's present age

s = son's present age

 

1)  m+4 = 3(s+4)

2)  m-4 = 5(s-4)

---------------------------------

1)  m+4 = 3s + 12

     m - 3s = 8         equation 1 reorganized

 

2)  m-4 = 5s - 20

     m - 5s = -16       equation 2 reorganized

 

Our system of equations is:

 

1)  m - 3s = 8

2)  m - 5s = -16

 

multiply equation 2 by -1 and add equations

 

1)  m - 3s = 8

    -m +5s = 16

    -------------------

           2s =  24

            s = 12

 

Son is currently 12 years old

 

substitute 12 in place of s in one of the original equations:

 

m - 3s = 8

m - 3(12) = 8

m - 36 = 8

m = 44

 

mother is currently 44 years old

 

You can check by plugging the values back into the

original equations.