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Math Help - Fraction Algebra

  1. #1
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    Fraction Algebra

    When 4 is subtracted from the numerator of a fraction, the value of the fraction becomes 2.

    When 5 is added to the denominator of the fraction, the value becomes 3/2. Find the fraction.

    My guess here is to undo the fraction by multiplying it..............
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  2. #2
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    Quote Originally Posted by Tren301 View Post
    When 4 is subtracted from the numerator of a fraction, the value of the fraction becomes 2.

    When 5 is added to the denominator of the fraction, the value becomes 3/2. Find the fraction.

    My guess here is to undo the fraction by multiplying it..............
    Call the fraction \frac{x}{y}.

    You're told that when 4 is subtracted from the numerator, the fraction is 2.

    So \frac{x - 4}{y} = 2

    x - 4 = 2y

    and when 5 is added to the denominator, the fracton is \frac{3}{2}.

    So \frac{x}{y + 5} = \frac{3}{2}

    2x = 3(y + 5)

    2x = 3y + 15.


    So now you have two linear equations

    x - 4 = 2y

    2x = 3y + 15.


    Solve them simultaneously, and then you can write what the fraction is.
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  3. #3
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    Hello Tren301
    Quote Originally Posted by Tren301 View Post
    When 4 is subtracted from the numerator of a fraction, the value of the fraction becomes 2.

    When 5 is added to the denominator of the fraction, the value becomes 3/2. Find the fraction.

    My guess here is to undo the fraction by multiplying it..............
    Let the fraction be \frac ab, and set up two simultaneous equations:
    \frac{a-4}{b}=2
    and
    \frac{a}{b+5}=\frac32
    Can you continue from here?

    Grandad

    PS Ah, I see Prove It has just pipped me to the post!
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  4. #4
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    Quote Originally Posted by Tren301 View Post
    When 4 is subtracted from the numerator of a fraction, the value of the fraction becomes 2.

    When 5 is added to the denominator of the fraction, the value becomes 3/2. Find the fraction.

    My guess here is to undo the fraction by multiplying it..............
    Hi Tren301,

    This word problem can be translated into equations.

    \frac{p-4}{q}=2

    \frac{p}{q+5}=\frac{3}{2}

    Can you solve the system?

    Edit: Ah we all posted at roughly the same time, but mine came out last.
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