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15 July, 02:59

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 6 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

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  1. 15 July, 04:44
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    The smallest integer that Pearl wrote down is 15.

    Step-by-step explanation:

    7 consecutive integers. They are:

    a

    a+1

    a+2

    a+3

    a+4

    a+5

    a+6

    Sum of the integers:

    a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6 = 7a + 21

    6 times the largest of the seven integers.

    The largest is a + 6. So

    7a + 21 = 6 (a + 6)

    7a + 21 = 6a + 36

    7a - 6a = 36 - 21

    a = 15

    The smallest integer that Pearl wrote down is 15.
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