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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $214$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

 Nov 4, 2023
 #1
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The integers can be represented as 

x       x+1      x+2       x+3      x+4     x+5    x+6     summed = 7x + 21   and this equals 214 (x+6) 

    7x+21 = 214 (x+6)

    7x + 21 = 214 x + 1284

     - 1263 = 207 x 

          x = 6  7/69                 <===== did you post your question with the correct numbers ? 

 Nov 5, 2023

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