Mathematics

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Find a fraction which reduces to 3/4 when the numerator and denominator are each decreased by 1, and which reduces to 4/5 when the numerator and denominator are each increased by 1.

  • Mathematics -

    Let the original fraction be x/y

    equation #1 : (x-1)/(y-1) = 3/4
    4x - 4 = 3y - 3
    4x - 3y = 1

    equation #2 : (x+1)/*(y+1) = 4/5
    5x + 5 = 4y + 4
    5x - 4y = -1

    #1 times 4 :16x - 12y = 4
    #2 times 3 : 15x - 12y = -3
    subtract them ...
    x = 7
    back in #1
    28 - 3y = 1
    -3y = -27
    y = 9

    the fraction was 7/9

    check:
    6/8 = 3/4 ✔
    8/10 = 4/5 ✔

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