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

 Jun 26, 2022
 #1
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The smallest integer is -17.

 Jun 26, 2022
 #2
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(n- 3)  +( n -2) + (n - 1)  + ( n ) +  (n+1) + ( n + 2) + (n + 3)  =   14 (n + 3)

 

7n = 14 (n + 3)     divide through by 7

 

n = 2 ( n + 3)

 

n = 2n + 6

 

n  -2n = 6

 

-n = 6

 

n = -6

 

The smallest integer  is   -6 - 3 =  -9

 

 

cool cool cool

 Jun 26, 2022
edited by CPhill  Jul 6, 2022

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