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21 January, 04:17

The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 114. If state A has more counties than state B, how many counties does each state have?

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  1. 21 January, 04:30
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    The number of counties in state A = 56

    The number of counties in state B = 58.

    Step-by-step explanation:

    Let the number of countries in state A = k

    So, the number of state in state B = (k+2)

    (as he next consecutive even integer after k is k + 2)

    Now, according to the question:

    k + (k+2) = 114

    or, 2k + 2 = 114

    ⇒ 2k = 114 - 2 = 112

    ⇒ k = 112/2 = 56

    or, k = 56

    Hence, the number of counties in state A = k = 56

    and the number of counties in state B = k + 2 = 56 + 2 = 58.
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