Question

the denominator of a rational number is greater than its numerator by 5. if the numerator is increased by 11 and the denominator is the decreased by 14, the new number becomes 5. find the original number.
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Answer 1

Answer:

Step-by-step explanation:

Given that,

the denominator of a rational number is greater than it's numerator by 5.

let the numerator of the rational number be x.

therefore it's denominator = x + 5

ATQ,

when the numerator is increased by 11 and the denominator is decreased by 14, then the number becomes 5.

➡ (x + 11)/(x + 5 - 14) = 5

➡ (x + 11)/(x - 9) = 5

➡ x + 11 = 5(x - 9)

➡ x + 11 = 5x - 45

➡ x - 5x = -45 - 11

➡ -4x = -56

➡ x = -56/-4

➡ x = 14

therefore,

numerator = x = 14

denominator = x + 5 = 19

hence, the original number is 14/19.

Answer 2

Answer:

Hope my answer helps you mate :-)

Step-by-step explanation:

Let numerator be x

Denominator be x+5

According to the question

$\frac{x + 11}{x - 9} = 5 \\ \\ x + 11 = 5x - 45 \\ \\ 4x = 56 \\ \\ x = 14$

14/19

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