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9 March, 20:48

The product of two consecutive integers is 5 more than three time the larger. What are the integers?

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  1. 9 March, 23:46
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    When calculating consecutive integers, the smaller number is x and the larger number is (x + 1).

    So the equation you can use is x + (x + 1) = 5 + 3 (x + 1)

    This is because the sum of the consecutive integers are equal to 5 more than 3 times the larger integer.

    Now simplify:

    x + (x + 1) = 5 + 3 (x + 1)

    2x + 1 = 5 + 3 (x + 1)

    2x + 1 = 5 + 3x + 3

    2x + 1 = 3x + 8

    Now isolate the variable:

    2x + 1 = 3x + 8

    Subtract 2x from both sides:

    1 = x + 8

    Subtract 8 from both side:

    -7 = x

    x = - 7

    So the smaller number is - 7 and the larger number is - 6.

    Now check your answer:

    -7 + (-7 + 1) = 5 + 3 (-7 + 1)

    -7 + (-6) = 5 + 3 (-7 + 1)

    -7 + (-6) = 5 + 3 (-7 + 1)

    -7 - 6 = 5 + 3 (-7 + 1)

    -13 = 5 + 3 (-7 + 1)

    -13 = 5 + 3 (-6)

    -13 = 5 + (-18)

    -13 = 5 - 18

    -13 = - 13

    This works!

    So the integers are - 7 and - 6.
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