The sum of three different numbers is 67. The two larger numbers differ by 7 and the two smaller numbers differ by 8. What is the value of the largest number?

 Aug 14, 2021


The sum of three different numbers is 67. The two larger numbers differ by 7 and the two smaller numbers differ by 8. What is the value of the largest number?     


Call the three numbers A, B, and C in the order from smallest to largest 


A                             B                               C  

|<------------ 8 ------------>|<------------ 7 ------------>|   


|<--------------------------- 67 ---------------------------->|                                                                  |  


A + (A + 8) + (A + 8 + 7)  =  67  

3A + 23                          =  67  

3A                                 =  67 – 23  

3A                                 =  44  

  A                                 =  44/3  =  14-2/3


A  =  14-2/3  

B  =  22-2/3  

C  =  29-2/3  


 Aug 14, 2021
edited by Guest  Aug 14, 2021


I came back today to see if the OP might have a follow up question.  What happened to my little visual representation?  The alignment is messed up.  Granted, I just used the space bar to align things but when I posted this yesterday it was perfect, the B was over the vertical line, so was the C.  If they hadn't been right, I'd have edited it so they were.  And what's that line way out there in space to the right.  I didn't put that there. 


Guest Aug 15, 2021

Hi Ron,


If you want to use spaces to align ASCII text in HTML documents, the first requirement is to be smarter than your computer.  LOL

Seriously, using spaces to align ASCII text in HTML documents is often an exercise in futility.


I’m glad you are still posting. Though you are not a member, I’ve followed your postings for about two years –well before our exchange here: https://web2.0calc.com/questions/the-sniper-story


To demonstrate that I’m serious and not broadcasting blarney, here are three (3) dozen links to your posts, randomly selected from more than 260 compiled over time up to November of 2020.  I’ve continued to add to the list, but the random selection is from that date.

Some of the posts in the compiled list may not be yours and I probably missed a few. The list was randomized twice using an online list randomizer, and then the first (36) were selected, so the sample is truly random.






































I was hoping you would have created a user name by now.  The user name “Ron Bosco” seems like a good choice. Bosco was the name of your cat during your childhood.  I think your cat would be pleased if you use that name.   Meow



I think it quite funny that my initials are the same as those of Gracie Allen. Good Night, GA

 Aug 21, 2021
edited by Guest  Aug 21, 2021


Hi Ginger.  It's wonderful to hear from you.  You keep track of my postings.  Since it's you, I'm flattered.  How do you know when it's me?  Do you recognize my style?  Or by the dot at the bottom?  I put the period down there, and color it white, just to add some white space at the bottom of the field.  It's been lonely not seeing any postings by you lately, or at least none in the easy problems which are all I'm capable of.  Ron 


 Aug 31, 2021

Hi Ron,


I definitely recognize your style. I have several lists with guests post links; though none have as many links as your file. The next closest are the BB (1-4) files, which I quit saving the links to years ago.  Most guest posters do not post for long, or they becomes members


I noticed your white dot early on. This made it very easy to confirm your posts, but about 3.5% of the posts I have in your list do not have this dot. So, either I’m wrongly attributing them to you, or you do not use the dot all time.  Also there are occasional posts on here that have a dot but do not seem like they belong to you.   



Demands on my time have reduced my posting; although in the past few weeks I have made a few posts as a guest; I’ll collect my copyrights at some point, except for the posts I don’t want cluttering up my profile. 

Here are three threads:


These threads have answers and troll post commentaries. 


There were two other troll posts; both of which were hidden. One was quite funny...

Along with the solution, I included an incidental commentary on WAT (Wrong Answer Troll) in this thread:


A guest comes along and “corrects” WAT’s wrong answer . . . with another wrong answer. I’m still debating whether it was WAT himself or just a random moron.   No escape!




You are capable of answering more than easy questions. Your solution for this logic question is a well-written master piecehttps://web2.0calc.com/questions/plz-don-t-cosplay-as-me-that-was-really-rude  You’ve developed excellent tutoring skills in the past two years.  I think it amazing you can remember and remove the oxidation from your high school mathematics after decades.


There is a subjective element to classifying the difficulty of math questions.  The binary description “easy” or “hard” is too broad. If one knows how to solve them, then it’s easy; if not, then it’s hard.


Several years ago I coded a program to scan and perform statistical analysis on the questions asked on web2.0calc’s forum.


Subjective Question classes:

*Category (0) –Mr. BB Interest Rate questions or arcane questions optimally answered with

                         Monty Carlo style or tabulated, logical resolution computer code. 

*Category (1) – Informal, simple non-homework, or curiosity based math question.

*Category (2) – Formal, simple homework.

*Category (3) – Formal, intermediate homework.

*Category (4) – Formal, advanced homework.

*Category (5) – Formal, AoPS (or related) homework.

*Category (6) – Formal, basic and intermediate physics, engineering, or chemistry.   

*Category (7) – Formal, advanced physics, engineering, or chemistry.   

*Category (8) – Formal, advanced collegiate mathematics or specialized math. (These are

                         very rare on this forum.)

*Category (9) – Social or non-math, Off Topic posts (includes posts with random characters).



Categories 2 through 8 are superlative in complexity.

Category (2) is generally elementary (up to grade 6 for US schools).

Category (3) is grades seventh through ninth

Category (4) is tenth through twelfth. This category also includes some first and second year collegiate math, which is taught in many high schools.    


Though not included in the list, Category (5) had three subcategories based on grade level corresponding to categories 2-4. AoPS questions are usually unique, and present questions at least one grade level ahead of the student’s grade. Generally, advanced AoPS questions enter well into the collegiate level. To teach AoPS math (whether online or in a classroom) for grades 2 through 7 requires at least a Master’s degree in mathematics. Teaching grades 8 through 12 requires a Ph.D. in mathematics.  The minimum requirements for AoPS tutors are to have completed or be in a final term of a four-year bachelor of mathematics or applied science degree, and have demonstrable skills in fourth year or higher collegiate mathematics. 



My program works (mostly) reasonably well, with about 20% of the questions needing reclassified up or down one increment. Posts with multiple questions throw exceptions. Multiple questions are usually in the same category.  Misspellings that are not in a misspelled-list throw exceptions. Some of the questions composed by teachers indicate communication skills that are so poor I wonder if they really know more than the students they are trying to teach.


Many questions that are identified as chemistry are actually physics questions.   Engineering questions are usually so closely related to physics questions they are indistinguishable. Very few physics and chemistry questions are on here anymore.  


The original scans yielded 3.4 as the average question category.  A recent scan in October of 2020 gave 2.8 as the average –it would not surprise me if it’s down to 2.2 now.  It’s amazing how many brain-dead, elementary questions are posted on here now. One reason for the low average is the massive repetition of elementary questions from remediated students. Very few of these questions are posted by elementary students; they are posted by middle and high school students in remedial classes. 


The teachers of these brain-dead students send them here –in droves. This is especially so since Covid has reduced classroom time to near nothing. But this infusion started long before Covid became a pandemic. Some of these remediated students repeat the same class, over and over, until they age out. Others are moved along with artificially inflated grades.


Here are recent examples of brain-dead, elementary questions:



This student needs a reading comprehension teacher, not a math teacher. 


This one is identified as “Advanced math”  https://web2.0calc.com/questions/advanced-math_1

It is advanced ...if you are in third grade. 


The irritation of having these students post their brain-dead questions on this forum gives credence to the thought that some of their teachers need intensive psychiatric care long before their careers would normally end.  Dumbness is not only contagious; continuous exposure can cause psychoses, suicidal ideation, and postal chaos. 


Some of these student s –those lacking academic skills in math, reading comprehension, and most other subjects will sometimes actually make it into a college or university. All public universities have quotas for various categories.  If necessary, universities will lower their admission standards while still selecting students who have a measurable probability of academic success. The artificially inflated grades help to move these poor students into the system. These exceptionally poor performing students are not common, but they do find their way in to university.


I run across one a couple of years ago while completing my master’s degree in psychology. I subbed for one my psychology professors while she attended a seminar. Normally I only taught the class on occasion as part of the master’s program, but this time I handled some of her academic appointments too. One of the appointments was the father of a failing student in an introductory psychology class, who made an appointment to plead for a passing grade for his son, who was a generally poor student on academic probation in his second year of eking out Ds and Cs in all his classes, except for the ones where he withdrew failing.  In this class, he was 6 points below the lowest score for a “D” grade.  She told me to handle it as I “see fit.”   I did.


The father thought I was the professor, I could tell the he had handled his son’s problems all his life. He was well practiced.  The father told me how his son was the “best and brightest” of all his children. To which I replied “Your other children must be major fuckups.”   Rather than being offended, he just nodded, saying, “They are.” One is in prison and the other is in drug rehab—for the third time. However, his daughter is holding a steady job as a clerk at Wal-Mart.  To me, she sounded like the only one who’s not a fuckup.. 


Some people are just not academically inclined.  I advised him to look into trade schools or apprenticeship programs for his son. Or better yet, let his son do the looking himself. Despite my professor saying to handle it as I see fit, she still makes the final decision. I don’t know what she gave him for a final grade, but when I relayed the disposition of the appointment to her, she said reflectively, “I wish I had the balls to be that blunt. ...”



This forum helps these brain-dead homework-moochers artificially advance into the mainstream, by creating the illusion they have mastered elementary math. 


On the bright side, this forum has many students who genuinely learn and practice their math skills by tutoring others. Among recent new members are two very skilled student tutors: catmg & amygdaleon305. Students of this caliber show up occasionally, but unfortunately they usually do not stay around for long. 



 Sep 4, 2021
edited by Guest  Sep 4, 2021

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