# Math Help - find age

1. ## find age

ten years ago,anns mother was four times older than her dauhter.after ten years the mother will be twice older than daughter.the present age of ann is

2. Originally Posted by hena
ten years ago,anns mother was four times older than her dauhter.after ten years the mother will be twice older than daughter.the present age of ann is
m-10 = 4(d-10)

m = 4d - 30

m+10 = 2(d+10)

4d - 30 + 10 = 2d + 20

2d = 40

d = 20

Ann is 20 years old.

3. Hello, hena!

Ten years ago, Ann's mother was four times older than Ann.
After ten years the mother will be twice as old as Ann.
Find the present age of Ann.

Let $A$ = Ann's present age.
Let $M$ = mother's present age.

Ten years ago, they were both ten years younger.
. . Their ages were: $A - 10\text{ and }M - 10$
We are told that: . $M-10\:=\:4(A-10) \quad\Rightarrow\quad M \:=\:4A - 30\;\;{\color{blue}[1]}$

Ten years hence, they are both ten years older.
. . Their ages are: $A + 10\text{ and }M + 10$
We are told that: . $M + 10 \:=\:2(A+10) \quad\Rightarrow\quad M \:=\:2A+10\;\;{\color{blue}[2]}$

Equate [1] and [2]: , $4A - 30 \:=\:2A + 10 \quad\Rightarrow\quad A \:=\:20$

Therefore, Ann is presently 20 years old (and her mother is 50).