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 !