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28 April, 08:28

If the product of two consecutive integers is decreased by 20 times the greater integer, the result is 442. find the integers

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  1. 28 April, 11:26
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    Let the first integer be x. Then the next consecutive integer is x+1.

    Translating the word problem into symbols, x (x+1) - 20 (x+1) = 442.

    Then x^2 + x - 20x - 20 = 442

    or x^2 - 19x - 462 = 0

    Solve by completing the square:

    x^2 - 19x + 90.25 - 90.25 - 462 = 0

    (x-9.5) ^2 - 552.25 = 0

    Taking the positive square root of both sides, we get x-9.5 = 23.5, or

    x = 33

    The two consecutive integers are 33 and 34.

    Check: (33) (34) - 20 (34) = 442 (as expected).
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