Question

11 years from now, the age of Peter will be half the square of the age he was 13 years ago. Calculate the current age of Peter.
[2 Marks]

Answer 1

Let Peter's current age = x years
$\therefore$ Age 13 years ago = $(x-13)$ years
Age 11 years later = $(x+11)$ years
[0.5 Marks]
According to the given statement
11 years later , the age of Peter = Half the square of the age he was 13 years ago
$\Rightarrow$ $(x+11)$ = $\frac{(x-13{)}^2}{2}$ [0.5 Marks]
$\Rightarrow$ $2x+22=x^2-26x+169$
$\Rightarrow$ $x^2-28x+147=0$
$\Rightarrow$ $x^2-(21+7)x+147=0$ [0.5 Marks]
$\Rightarrow$ $x^2-21x-7x+147=0$
$\Rightarrow$ $x(x-21)-7(x-21)=0$
$\Rightarrow$ $x=21orx=7$

Since Peter's age can't be 7 years
$\therefore$ His current age = 21 years [0.5 Marks]