Algebra

 

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) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)  =  (28 / 9)(x+6)    

 

                                                                 7x + 21  =  (28x + 168) / 9    

 

                                                          9 • (7x + 21)  =  (28x + 168)    

 

                                                              63x + 189  =  28x + 168    

 

                                                                        35x  =  – 21    

 

                                                                            x  =  – 21 / 35    

 

                                                      reduces to     x  =  – 3 / 5    

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