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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is euqal to 14 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

 Nov 13, 2022
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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is euqal to 14 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?  

 

Say that "x" is the smallest number.  Then subsequent integers add 1 to the integer before it.  

 

(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) = (14)(x+6)      solve for x  

 

                                                                 7x + 21 = 14x + 84  

 

                                                                 21 – 84 = 14x – 7x  

 

                                                                          7x = –63                 x  =  –9  

 

Check answer  

                                    Does   (–9) + (–8) + (–7) + (–6) + (–5) + (–4) + (–3) = (14)(–3)  ?  

 

                                    Does   –42 = –42  ?   Yes.  Solution is correct.  

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 Nov 13, 2022

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