[tex]\huge{ \green{\bold{\underline {\underline {\orange {♕︎Ⱥ \: question}}}}}}[/tex]
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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Answers & Comments
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
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Let denominator be y
Numerator be 5y - 3
The fraction
[tex] \frac{(5y - 3)}{y} [/tex]
ACCORDING TO THE QUESTION
[tex] \frac{(5y - 3) - 2}{y +7 } = \frac{5}{3} [/tex]
[tex] \frac{5y - 5}{y + 7} = \frac{5}{3} [/tex]
=> 3(5y -5) = 5(y+7)
=> 15y - 15 = 5y + 35
=> 15y - 5y = 35 + 15
=> 10y = 50
[tex]y = \frac{50}{10} [/tex]
[tex]y = 5[/tex]
Denominator = 5
Numerator =
5(5) - 3
25 - 3
22
The original rational number is :
[tex] \frac{22}{5} [/tex]
Therefore, the rational number is
[tex] \frac{22}{5} [/tex]
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