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31 March, 08:11

The sum of two numbers is 24. If 4 less than 6 times the smaller number equals 5 more than 3 times the larger, what are the numbers?

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  1. 31 March, 09:35
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    Let x = smaller number, y = larger number

    The first statement is expressed as

    x + y = 24

    The second statement is expressed as

    6x - 4 = 3y + 5

    Solving for x by substituting the first equation of terms of y which is y = 24 - x,

    6x - 4 = 3 (24 - x) + 5

    6x - 4 = 72 - 3x + 5

    6x + 3x = 72 + 5 + 4

    9x = 81

    x = 81/9 = 9

    Solving for y,

    y = 24 - 9 = 15

    So the numbers are 9 and 15.
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