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13 December, 03:50

Find two consecutive odd numbers such that the sum of one-fifth of the smaller and forth-sevenths of the larger is equal to fifty-nine

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  1. 13 December, 05:36
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    Two consecutive odd numbers are 75 and 77.

    Step-by-step explanation:

    Let's assume the two consecutive odd numbers are A and B such that A > B and their difference is 2, i. e. A - B = 2.

    It say the sum of one-fifth of the smaller and forth-sevenths of the larger is equal to fifty-nine, i. e. (4/7) A + (1/5) B = 59.

    Simplifying the equation: - 20A + 7B = 2065.

    We have a system of equations: - A - B = 2 and 20A + 7B = 2065.

    Using Substitution method and substitute A = B + 2 into second equation:-

    20 (B+2) + 7B = 2065

    20B + 40 + 7B = 2065

    27B = 2065-40 = 2025

    B = 2025/27 = 225/3 = 75.

    Then, A = B+2 = 75+2 = 77.

    Hence, two consecutive odd numbers are 75 and 77.
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