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Question
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.
Solution
Let take Rohan's age = x years
Hence, his mother's age = x + 26
3 years from now
Rohan's age = x + 3
Age of Rohan's mother will = x + 26 + 3 = x + 29
The product of their ages 3 years from now will be 360 so that
(x + 3)(x + 29) = 360
⇒ x2 + 29x + 3x + 87 = 360
⇒ x2 + 32x + 87 = 360
⇒ x2 + 32x = 273
⇒ x2 + 32x - 273 = 0
⇒ x2 + 39x - 7x - 273 = 0
⇒ x(x + 39) - 7(x + 39) = 0
⇒ (x + 39)(x - 7) = 0
⇒ x + 39 = 0 and x - 7 = 0
⇒ x = -39 and x = 7
Since,
Current age of Rohan = 7 year
Age of Rohan's mother = x + 26
= 7 + 26
= 33 year
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