Question

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​

Answer 1

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 :-

The present age of Rohan.

Solution :-

Let the age of Rohan be 'x'

Then, Rohan’s mother’s age = x + 26

After 3 years,

Age of Rohan’s = x + 3

Age of Rohan’s mother will be = x + 26 + 3 = x + 29

Given that,

The product of their ages after 3 years will be equal to 360.

According to the question,

$\sf (x + 3)(x + 29) = 360$

$\sf x^{2}+(3+29)x+87=360$

$\sf x^{2}+32x-273=0$

$\sf x^{2}+39x-7x-273=0$

$\sf x(x+39)-7(x+39)=0$

$\sf (x+39)(x-7)=0$

$\sf x = 7$

Therefore, Rohan's present age is 7 years.

Answer 2

Let us consider,

The first integer number = x

Thus, the next consecutive positive integer will be = x + 1

Product of two consecutive integers = x × (x +1) = 306

⇒ x2 + x = 306

⇒ x2 + x – 306 = 0

Therefore, the two integers x and x+1, satisfies the quadratic equation, x2 + x – 306 = 0, which is the required representation of the problem mathematically.