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# 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?

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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