Question

If Zeba were younger by $5$ years than what she really is, then the square of her age (in years) would have been $11$ more than five times her actual age. What is her age now?

Answer 1

Step 1: Establish the equation:

Let the age of Zeba be $x$.

According to the conditions given in the question, the equation will be

${\left(x-5\right)}^2=11+5x$

Step 2: Solve the equation:

On solving this equation we get;

${\left(x-5\right)}^2=11+5x$

$\Rightarrow$ $x^2-10x+25=11+5x$

$\Rightarrow$ $x^2-15x+14=0$

$\Rightarrow$ $x^2-14x-x+14=0$

$\Rightarrow$$x\left(x-14\right)-1\left(x-14\right)=0$

$\Rightarrow$ $\left(x-14\right)\left(x-1\right)=0$

$\Rightarrow$ $x=14,1$

If Zeba's age is $1$, her being $5$ years younger is not possible.

$\therefore x=14$

Hence, the actual age of Zeba is $14$.