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22 January, 08:44

5/y + 7/x = 24

12/y + 2/x = 24, find the ratio of x to y.

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  1. 22 January, 08:53
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    Step-by-step explanation:

    5/y + 7/x = 24 ... (1)

    12/y + 2/x = 24 ... (2)

    Let 1/y = a and 1/x = b

    5a + 7b = 24 ... (3)

    12a + 2b = 24 ... (4)

    Multiply (3) by 2 and (4) by 7

    10a + 14b = 48 ... (5)

    84a + 14b = 168 ... (6)

    Substracting (5) from (6)

    84a - 10a = 168 - 48

    74a = 120

    a = 120/74

    a = 60/37

    Putting a = 60/37 in (3)

    5a + 7b = 24

    5 (60/37) + 7b = 24

    300/37 + 7b = 24

    Multiply each term 37

    300 + 259b = 888

    259b = 888 - 300

    259b = 588

    b = 588/259

    And a = 1/y

    60/37 = 1/y

    Cross multiply

    60y = 37

    y = 37/60

    Also

    b = 1/x

    588/259 = 1/x

    Cross multiply

    588x = 259

    x = 259/588
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