Question

Ann is 12 years old. Her mother is 3 times as old as Ann. How many years ago was her mother 4 times as old as Ann?

Answer 1

4 years ago

Explanation:

If we call Ann´s age A and mother´s age M:

`A = 12`

`A * 3 = M`

, a few years back ( Y ):

`( A - Y ) * 4 = ( M - Y )`

So, by substitution:

`( A - Y ) * 4 = ( A * 3 - Y )`

`4A - 4Y = 3A - Y`

`4A - 3A = 4Y - Y`

`A = 3Y`

`Y = A/3 = 12/3= 4`

Answer 2

`4` years ago.

Explanation:

We know both of their present ages.

If Ann is `12` years old, then her mother is `3xx 12=36` years old.

A number of years ago,they were both younger.
Let the number of years be `x`.

Ann's age was `12-x` and her mother's age was `36-x`

`36-x =4(12-x)" "larr` the mom was `4` times older,

`36-x = 48-4x`

`4x-x = 48-36`

`3x = 12`

`x=4`

It was `4` years ago.

Check: Ann was `8` and her mom was `32`

`4 xx8 = 32`