Question

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The numerator of a rational number is 3 less than five times its denominator. When 2 is subtracted from its numerator, and 7 is added to its denominator, the simplest form of the rational number obtained is 5/3. Find the original rational number.

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Answer 1

Let the denominator be x

ATQ ,

(5x-3-2)/(x+7) = 5/3

15x - 15 = 5x + 35

10x = 50

x = 5

The original rational no. is 22/5

Answer 2

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Let denominator be y

Numerator be 5y - 3

The fraction

$\frac{(5y - 3)}{y}$

ACCORDING TO THE QUESTION

$\frac{(5y - 3) - 2}{y +7 } = \frac{5}{3}$

$\frac{5y - 5}{y + 7} = \frac{5}{3}$

=> 3(5y -5) = 5(y+7)

=> 15y - 15 = 5y + 35

=> 15y - 5y = 35 + 15

=> 10y = 50

$y = \frac{50}{10}$

$y = 5$

Denominator = 5

Numerator =

5(5) - 3

25 - 3

22

The original rational number is :

$\frac{22}{5}$

Therefore, the rational number is

$\frac{22}{5}$

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