Question

the sum of the ages of Vivek and his younger brother Amit is 47 years .the product of their ages is 550.find their ages

Answer 1

Solution :

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Given :

Statement 1 :
The sum of the ages of Vivek and his younger brother Amit is 47 years.,.

⇒ Let the age of  Vivek be x,.

Then,.

⇒ The age of amit = 47 - x ,

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Statement 2 :

The product of their ages is 550.

So,

We can say that,.

⇒ x (47 - x) = 550 ....(1)

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To find :

Their present ages :

(That is : the value of x & 47 - x,.)

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So,.

We can also say that,.

⇒ x(47 - x) = 550

⇒ 47x - x² = 550

⇒ 47x - x² - 550 = 0

⇒ -x² + 47x - 550 = 0

⇒ -(x² - 47x + 550) = 0

⇒ x² - 47x + 550 = 0

⇒ x² - 22x - 25x + 550 = 0

⇒ x(x - 22) - 25(x - 22) = 0

⇒ (x - 25)(x - 22) = 0,.

For the equation to be 0,.

Either,

⇒ x - 25 = 0 (or) x - 22 = 0

⇒ x = 25 (or) x = 22

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As, 47 - 25 = 22 & 47 - 22 = 25,.

⇒ ∴ The present ages of Vivek & Amit are 22 & 25,.

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                                           Hope it Helps !!

⇒ Mark as Brainliest,.

Answer 2

Answer :

Given : sum of their ages = 47 yrs

Let vivek's age be x

then, amit's age= (47-x) yrs

ATQ

x (47-x) = 550

47x - x = 550

x2 -47x +550 = 0

x2 - 25x -22x +550. = 0

x( x-25) - 22 (x-25) = 0

( x-25) (x-22). =0

hence x = 25 or 22

When x = 22

vivek's age= 22 yrs

amit's age= 25 yrs

When x = 25

vivek's age= 25 yrs

amit's age= 22 yrs

But as vivek is elder brother his age will be 25 yrs

so then , amit's age will be 22 yrs

[U can solve the quadratic equation using quadratic formula also l have solved it using middle term splitting method]

Hope this ans would help you

Thank u ☺️☺️