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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/9 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

 May 31, 2024
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(n-3) + (n-2) + (n-1) + n + (n+1) + (n+2) + (n+ 3)  =  (28/9)(n + 3)

 

7n  = (28/9)(n + 3)

 

7n = (28/9)n + 28/3

 

63n = 28n + 84

 

63n - 28n = 84

 

35n = 84

 

n = 84 / 35  =  12 / 5

 

(n - 3)  = (12/5 - 3)  =  -3 / 5      (which is NOT an integer !!! )

 

cool cool cool

 May 31, 2024

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