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