the denominator of a fraction is greater than its numerator by 9.if 7 is subtracted from both,its numerator and denominator, the fraction be

Question

the denominator of a fraction is greater than its numerator by 9.if 7 is subtracted from both,its numerator and denominator, the fraction becomes 2/3.find the original fraction.

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Parker 4 months 2021-09-24T21:07:30+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-24T21:08:50+00:00

    Answer:

    25/34

    Step-by-step explanation:

    let the numerator be x

    so the denominator is x+9

    ATQ

    ⇒x-7/x+9-7=2/3

    ⇒x-7/x+2=2/3

    ⇒3(x-7)=2(x+2)

    ⇒3x-21=2x+4

    ⇒3x-2x=4+21

    ∴x=25

    so the numerator is 25 and denominator is 25+9=34

    so the number is 25/34

    0
    2021-09-24T21:09:17+00:00

    Answer:

    Step-by-step explanation:

    Let x=numerator,

    y=denominator.

    y=x+7 – – – – – (i)

    (x+3)/(y+3) = 2/3

    (Cross multiply)

    3(x+3)=2(y+3)

    3x+9=2y+6

    (subtract 9 from both sides)

    3x+9–9=2y+6–9

    3x=2y+6–9

    3x=2y-3 – – – – – – – (ii)

    (substitute the value of equation (i) into (ii))

    3x=2(x+7)-3

    3x=2x+14–3

    3x=2x+11

    (subtract 2x from both sides)

    3x-2x=2x+11–2x

    x=11.

    (substitute the value of x into equation (i))

    y=7+11

    y=18.

    so numerator =11,

    denominator = 18.

    So original fraction is 11/18.

    3/11th of original fraction is

    = 11/18 x 3/11

    = (11×3)/(18×11)

    = 3/18

    =1/6

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