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 5 times her actual age. What is her age now?
Given:
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 5 times her actual age.
To do:
We have to find her present age.
Solution:
Let the present age of Zeba be $x$ years.
This implies,
Age of Zeba if she was 5 years younger$=x-5$ years
According to the question,
$(x-5)^2=5x+11$
$x^2-10x+25=5x+11$
$x^2-10x-5x+25-11=0$
$x^2-15x+14=0$
Solving for $x$ by factorization method, we get,
$x^2-14x-x+14=0$
$x(x-14)-1(x-14)=0$
$(x-14)(x-1)=0$
$x-14=0$ or $x-1=0$
$x=14$ or $x=1$
Zeba's age cannot be $1$ year. Therefore, the value of $x$ is $14$.
$x-5=14-5=9$
The present age of Zeba is $14$ years.
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