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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 21 / 4 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?   

 

Let the first integer be represented by x.   

Since the integers are consecutive, each following   

integer is one more than the integer before it.  

 

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

 

                                                                                21x + 126  

                                                             7x + 21  =  –––––––––   

                                                                                      4          

Multiply both sides by 4    

                                                            28x + 84  =  21x + 126               

Subtract 21x from both sides   

                                                              7x + 84  =            126               

Subtract 84 from both sides                     

                                                                      7x  =  42    

Divide both sides by 7    

                                                                        x  =  6    

 

check answer    

                               6 + 7 + 8 + 9 + 10 + 11 + 12  =  (21/4)(12)  

                                                                       63  =  63   

.

Jul 17, 2023
 #3
 #5
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For the record, Post #3, signed by GA, is not by the real GA.

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Hi Melody,

This imposter, who either escaped from a loony bin, or a Scooby Doo cartoon, or both, is the forum’s original WAT (Wrong Answer Troll).

 

Two years ago, in this post https://web2.0calc.com/questions/i-know-this-is-kind-of-easy-but-i-m-stuck, I made the first of several comments about him and gave him the name “WAT”.   I concluded that post with these comments:

One open question is how he will react to this post, assuming he sees it. There is always a reaction; it’s not always obvious.

Within a few months his reaction became clear: He creates vulgar and crude social troll posts and signs my initials.  Here’s a link to one of them:  https://web2.0calc.com/questions/help-please_9275. The relevant posts are invisible to the public, but you can see them, of course. This is just one of many such posts. Here are comments I made about some of them.  https://web2.0calc.com/questions/hmmt-november-2021-problem-6-general-round#r4

 

Lately, in the past week or so, WAT has signed my initials to some of his single-line BS math answer posts, and several social posts, some written in bombastic prose, one of which is quite funny.  I can deal with this “identity theft;” it’s worth the annoyance and aggravation to communicate with him –at least for now.

 

I post disclaimers mostly as a formality, and mainly for those who are unfamiliar with my math and social postings. I estimated that most of the long-time members and guests would recognize my style enough to know these posts are not mine, such as Ron did on this post. But because I’ve used my initials when posting as a both guest and member they have become iconic. So when most anyone who sees them on a post, GingerAle is brought to mind without regard to what is posted. Such was the case for the post above. 

 

It’s worth noting that if I made an anonymous post within the range of my normal posting style, you’d instantly recognize me. Remember this:https://web2.0calc.com/questions/math_42782#r12  Here, you recognized me nearly instantly even though I’d made only a few prior posts. But it often doesn’t work the other way around: a single line post with an absurd answer (a troll post) in a style I’ve never used is instantly assigned to me because my initials are appended to it.

 

...This could be an interesting “brand” recognition psychology study.  !

 

------------

Guest poster #1 is Mr. BB.  He often answers such questions with his computer.

This question is ideally suited for a computer, and is very difficult to solve without one.

The divisor counts and the product of the divisors are correct.  (It’s a little more than (34)).

-----------------

GA

--. .- 

Jul 17, 2023
Jul 16, 2023

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