Question

Find two numbers with the condition that their sum, 8 is four times their difference?

Answer 1

Suppose x and y be the two numbers, with x being greater of the two.

From question:

                            x + y = 8                           

                                 x  = 8 - y            Eq. I

         and  4 (x - y) = x + y               

⇒ 4x - 4y = x + y

⇒ 3x - 5y = 0 Eq. II

 

Substitute value of x from Eq. I in Eq. II:

3 ( 8 - y) - 5y = 0

⇒ 24 - 3y - 5y = 0

⇒ 24 - 8y = 0

⇒ 8y = 24

⇒ y = 24/8 =3

 

Substitute y = 3 in Eq. I:

x  =  8 - 3 = 5

 

Thus, the two numbers satisfying the conditions are: 5 and 3

The two numbers satisfying the conditions are: 5 and 3.