Represent the following situation in the form of a quadratic equation:
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.
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.
(N/A) Let Rohan's present age be $x$ years.
Then,his mother's present age $= x + 26$ years.
After $3$ years:
Rohan's age $= x + 3$ years.
Mother's age $= (x + 26) + 3 = x + 29$ years.
According to the problem,the product of their ages after $3$ years is $360$.
Therefore,$(x + 3)(x + 29) = 360$.
Expanding the equation: $x^2 + 29x + 3x + 87 = 360$.
$x^2 + 32x + 87 - 360 = 0$.
$x^2 + 32x - 273 = 0$.
Then,his mother's present age $= x + 26$ years.
After $3$ years:
Rohan's age $= x + 3$ years.
Mother's age $= (x + 26) + 3 = x + 29$ years.
According to the problem,the product of their ages after $3$ years is $360$.
Therefore,$(x + 3)(x + 29) = 360$.
Expanding the equation: $x^2 + 29x + 3x + 87 = 360$.
$x^2 + 32x + 87 - 360 = 0$.
$x^2 + 32x - 273 = 0$.
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