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?

2 Answers
May 11, 2018

4 years ago

Explanation:

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

A=12

A3=M

, a few years back ( Y ):

(AY)4=(MY)

So, by substitution:

(AY)4=(A3Y)

4A4Y=3AY

4A3A=4YY

A=3Y

Y=A3=123=4

May 11, 2018

4 years ago.

Explanation:

We know both of their present ages.

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

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

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

36x=4(12x) the mom was 4 times older,

36x=484x

4xx=4836

3x=12

x=4

It was 4 years ago.

Check: Ann was 8 and her mom was 32

4×8=32