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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 8 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

 Apr 26, 2023
 #1
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n + n + 1 + n + 2 + n + 3 + n + 4 + n + 5 + n + 6 ==8 * [n + 6], solve for n

 

7n + 16 =8n + 48

7n - 8n ==48 - 16

 - n = 32 or:

n == - 32 - the smallest n

 Apr 26, 2023
 #3
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should be 7n + 21  ....  not 16  

 

otherwise, good work --- if you'd checked the answer, you'd probably have caught that  

.

Guest Apr 26, 2023
edited by Guest  Apr 26, 2023
 #2
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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 8 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?  

 

Since the integers are consecutive, each integer's value will be one more than the integer before. 

 

let x be the first integer

 

then the seven integers are  (x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)

 

                   and their sum is  7x + 21  

 

we want this to be 8 times the largest number  

 

                                         so  7x + 21  =  8 times (x+6)  

 

                                               7x + 21  =  8x + 48  

 

                                               7x  – 8x  =  48 – 21  

 

                                                       – x  =  27

 

                                                          x  =  –27    

 

check answer by plugging 

into the original equality          7x + 21  =  8 times (x+6)  

 

                                       (7)(–27) + 21  =  (8)(–27) + 48  

 

                                            –189 + 21  =  –216 + 48  

 

                                                     –168  =  –168               looks good 

.

 Apr 26, 2023

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