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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?

 Jul 2, 2024
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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?   

 

                                                                                              (x + 6)    28   

(x)  +  (x+1)  +  (x+2)  +  (x+3)  +  (x+4)  +  (x+5)  +  (x+6)  =  ––––– • –––   

                                                                                                  1         9   

                                28x + 168   

             7x + 21  =  –––––––––   

                                      9    

 

          63x + 189  =  28x + 168       

 

                     35x  =  – 21   

 

                                 – 21            3  

                         x  =  ––––  =   –––      

                                   35             5    

 

                   The solution is not an integer, so the    

                   problem, as written, is not satisfied.   sad    

 

                   Assuming the problem can be solved,   

                   I hope someone will show me my error.    

.

 Jul 3, 2024

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