algebra

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the product of two consecutive even integersis 34 less than 7 times their sum.find the two integers.

  • algebra -

    let the first integer be x
    then the second even integer is x+2

    x(x+2) = 7(x + x+2) - 34
    x^2 + 2x = 14x + 14 - 34
    x^2 - 12x + 20 = 0
    (x-10)(x-2) = 0
    x = 10 or x = 2

    the numbers are 10 and 12 or the numbers are 2 and 4

    check:
    case 1: numbers are 10 and 12
    product = 120
    7 times their sum = 154
    is 120 less than 154 by 34 ? YES

    case 2: numbers are 2 and 4
    product = 8
    7 times their sum = 42
    is 8 less than 42 by 34 ? YES!

    So we have two answers:
    the integers could be 10 and 12
    or
    the integers could be 2 and 4

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