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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $21$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

 Aug 2, 2023

Best Answer 

 #1
avatar+676 
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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $21$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?   

 

Let the smallest integer be represented by x.   

Since the integers are consecutive, each following   

integer is one larger than the integer before it.  

 

(x)  +  (x + 1)  +  (x + 2)  +  (x + 3)  +  (x + 4)  +  (x + 5)  +  (x + 6)  =  (21) • (x + 6)    

 

                                                             7x + 21  =  21x + 126   

Subtract 7x from both sides   

                                                                     21  =  14x + 126               

Subtract 126 from both sides                     

                                                                  –105  =  14x   

Divide both sides by 14   

                                                                        x  =  –7.5   

 

check answer    

                         (–7.5) + (–6.5) + (–5.5) + (–4.5) + (–3.5) + (–2.5) + (–1.5)  =  (21) • (–1.5)        

                                                                                                           –31.5  =  –31.5  

 

.

 Aug 2, 2023
 #1
avatar+676 
+1
Best Answer

 

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $21$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?   

 

Let the smallest integer be represented by x.   

Since the integers are consecutive, each following   

integer is one larger than the integer before it.  

 

(x)  +  (x + 1)  +  (x + 2)  +  (x + 3)  +  (x + 4)  +  (x + 5)  +  (x + 6)  =  (21) • (x + 6)    

 

                                                             7x + 21  =  21x + 126   

Subtract 7x from both sides   

                                                                     21  =  14x + 126               

Subtract 126 from both sides                     

                                                                  –105  =  14x   

Divide both sides by 14   

                                                                        x  =  –7.5   

 

check answer    

                         (–7.5) + (–6.5) + (–5.5) + (–4.5) + (–3.5) + (–2.5) + (–1.5)  =  (21) • (–1.5)        

                                                                                                           –31.5  =  –31.5  

 

.

Bosco Aug 2, 2023

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