Question

A woman is now 8 times as old as her son Michael. Two years ago, she was 15 times as old as Michael. Form an equation and solve it.

Answer 1

w = the woman's age
m = michael's age

8m = w
15(m -2) = (w-2)

15(m - 2) = (8m - 2)
15m - 30 = 8m - 2
15m - 8m - 30 = 8m - 8m - 2
7m - 30 = -2
7m - 30 + 30 = -2 + 30
7m = 28
m = 4

8m = w
8(4) = w
32 = w

w = 32 years old
m = 4 years old

Answer 2

-- Let's call Michael's age 'S'  (for 'son')

-- Right now his mother's age is 8 times his age ... 8s

-- Two years ago ...

                   son was (S - 2) years old

                   mother was  (8s -2) years old.

                   she was 15 times her son's age.

--  So          (8s - 2)  =  15(s - 2)    <=== this is the equation

                    8s - 2   =  15s - 30

                        - 2   =    7s - 30

                        28   =    7s

                          4   =     s        <=== this is the solution to the equation

-- Michael is  4  now.
   His mother is  (8s) = 32

-- Two years ago, Michael was  2 .
    His mother was (8s - 2) = 30

   30  = 15 x 2      yay !