Thread: Maths

Hi could someone please explain the easiest way to work this question out?

In three years time Ann will one third of her mother's age. In another 18 years from now, Ann will be half her mother's age. How old is her mother now??

Hello, Spixol1231

Three years from now, Ann will one-third of her mother's age.
Eighteen years from now, Ann will be half her mother's age.
How old is her mother now?

Let $\displaystyle A$ = Ann's age now.
Let $\displaystyle M$ = Mom's age now.

Three years from now, they will both be 3 years older.
. . Ann will be $\displaystyle A + 3$ years old.
. . Mom will be $\displaystyle M+3$ years old.

At that time, Ann's age is one-third Mom's age.
. . $\displaystyle A + 3 \:=\:\tfrac{1}{3}(M+3) \quad\Rightarrow\quad {\color{blue}M - 3A \:=\:6}$


Eighteen years from now, they will both be 18 years older.
. . Ann will be $\displaystyle A+18$ years old.
. . Mom will be $\displaystyle M + 18$ years old.

At that time, Ann's age is one-half Mom's age.
. . $\displaystyle A + 18 \:=\:\tfrac{1}{2}(M+18) \quad\Rightarrow\quad {\color{blue}M - 2A \:=\:18}$

Now solve the system of equations.

Thanks heaps