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Represent the following situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
Given :
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360.
To find :
We have to find Rohan’s present age.
Solution :
Let the present age of Rohan be $x$.
This implies,
The age of the mother $= x+26$
Age of the Rohan after 3 years $= x+3$
Age of the mother after 3 years $=(x+26)+3=x+29$.
Therefore,
$(x+3)(x+29) = 360$
$x(x+29)+3(x+29) = 360$
$x^2+29x+3x+87 = 360$
$x^2+32x+87-360 = 0$
$x^2+39x-7x-273=0$
$x(x+39)-7(x+39)=0$
$(x+39)(x-7)=0$
$x+39=0$ or $x-7=0$
$x=7$ or $x=-39$ which is not possible
The present age of Rohan is $7$ years.
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