Question

Find the whole number which when decreased by 20 is equal to 69times the reciprocal of the number.

Answer 1

let the number be x. thenx - 20 = 69/x .                        
[reciprocal of x will be 1/x]
if we solve it then we get the following quad equation.
x2 - 20x - 69 = 0
x2 - 23x + 3x - 69 = 0
x(x - 23) + 3 (x - 23) = 0
thus, x = 23 , -3.

Answer 2

according to the question,

let the whole number be x then

⇒x-20=69(1/x)

⇒x-20=69/x

⇒x-69/x=20

⇒x²-69/x=20

⇒x²-69=20x

⇒x²-69-20x=0

⇒x²-23x+3x-69

⇒x(x-23)+3(x-23)

⇒(x+3)(x-23)

therefore x=-3 and x=23