Question

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

Answer 1

Let the whole number be x as it is decreased by 20

⇒ (x - 20) = 69. (1/2)

⇒ 𝑥. 20 = 69. (1/𝑥)

⇒ 𝑥(𝑥 - 20) = 69

⇒ 𝑥² - 20𝑥 - 69 = 0

⇒ 𝑥² - 23 + 3𝑥 - 69 = 0

⇒ 𝑥(𝑥 - 23) + 3(𝑥 - 623) = 0

⇒ (x - 23) (x + 3) = 0

⇒ x = 23; x = -3

As the whole numbers are always positive, x = -3 is not considered.

∴ The whole number x = 23.