The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers.

Question

The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers.

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Diễm Thu 5 years 2021-07-25T16:26:15+00:00 1 Answers 67 views 0

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  1. minhkhang
    0
    2021-07-25T16:27:46+00:00
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    9514 1404 393

    Answer:

    • (x -3) +(x -1) +(x +1) +(x +3) = -72
    • -21, -19, -17, -15

    Step-by-step explanation:

    Let x represent the even integer between the middle two odd integers. Then the sum of the four odd integers is …

      (x -3) +(x -1) +(x +1) +(x +3) = -72

      4x = -72

      x = -18

    The four integers are -21, -19, -17, -15.

    _____

    Additional comment

    You could let x represent one of the integers. Often, people choose to let it represent the least of them. Then the equation becomes x +(x+2) +(x+4) +(x+6) = -72, so 4x = -84 and x = -21. This introduces a “subtract 12” step in the solution process that is unnecessary if x is chosen to be the average of the integers.

    As the average, x is the sum divided by the number of them, so you know x=-72/4 = -18 immediately. Then you just have to find the nearest two odd integers below and above -18. You can do the whole problem mentally.

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