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

1.	Find the whole number which when decreased by 20 is equal to 69 times the reciprocal of the number.
Answer» Let the whole number be x. When it is decreased by 20 ⇒(x – 20) And, the reciprocal of the whole number is \(\frac{1}{x}\) From the given condition, we have (x – 20) = 69 x (\(\frac{1}{x}\)) ⇒ x(x – 20) = 69 ⇒ x² – 20x – 69 =0 Solving for x by factorization method, we have ⇒ x² – 23x + 3x – 69 = 0 ⇒ x(x – 23) + 3(x – 23) = 0 ⇒ (x – 23)(x + 3) = 0 Thus, x is either 23 Or -3 As we that a whole number is always positive, x = – 3 is not considered. Therefore, the whole number is 23.

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

Answer»

Let the whole number be x.

When it is decreased by 20 ⇒(x – 20)

And, the reciprocal of the whole number is \(\frac{1}{x}\)

From the given condition, we have

(x – 20) = 69 x (\(\frac{1}{x}\))

⇒ x(x – 20) = 69

⇒ x² – 20x – 69 =0

Solving for x by factorization method, we have

⇒ x² – 23x + 3x – 69 = 0

⇒ x(x – 23) + 3(x – 23) = 0

⇒ (x – 23)(x + 3) = 0

Thus, x is either 23 Or -3

As we that a whole number is always positive, x = – 3 is not considered. Therefore, the whole number is 23.