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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?

 Jul 10, 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?

 

This is simple, but long winded. 

 

Call the first integer    x  

then the 2nd is           x + 1 

then the 3rd is            x + 2 

then the 4th is            x + 3 

then the 5th is            x + 4 

then the 6th is            x + 5 

and the 7th is             x + 6  

 

Add them all together and you get 7x + 21    

 

The problem also says their sum equals 14 times the largest integer, which is expressed as (14)(x + 6)  

 

Set the two equal to each other  7x + 21 = 14x + 84 

 

Subtract 7x from both sides                21 = 7x + 84  

 

Subtract 84 from both sides              – 63 = 7x  

 

Divide both sides by 7                           x = – 9  

 

Check answer  

                          – 9 

                          – 8 

                          – 7 

                          – 6 

                          – 5 

                          – 4 

                          – 3 

total is              – 42

 

is (14)(– 3) also – 42 ?   Yes, so the answer is confirmed.  

.

 Jul 11, 2022

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