A little background here: I have (somewhat stupidly) offered to assist 11 year old, 5th grader Grandson with his homework.
(No, this isn’t Grandson. It’s from a stock photo online. It’s here: http://www.bing.com/images/search?q=Pictures+of+kids+doing+homework&qpvt=Pictures+of+kids+doing+homework&FORM=IGRE#view=detail&id=20A8F8F0CB3FCDE22C672DBBB14590BB04238535&selectedIndex=35
There, go click on that! ha!)
To that end, he brought it to our house yesterday and we began—of course, after a snack and some small talk and deciding whether or not it was okay to keep one’s socks on whilst one’s shoes were off—in MY house not exactly known for its clean floors what with Security and TMWLH* tracking in leaves (see another post on that one) and whatnot…….but I digress.
(*TMWLH = the Man Who Lives Here)
Wait a minute, what was the question?
Oh. I haven’t gotten to the question yet…….
So there we were, diligently (although with difficulty) going through math word problems.
We managed to struggle through the majority of them when this problem came up in his homework: (I will paraphrase since I don’t have the actual problem directly in front of me.)
Susie wants to start a swim club. (What? It’s fall—why would she want to start a swim club in the fall? Must belong to one of those private clubs with pools inside or else the YMCA which has a swim club, I think, already, but never mind…….)
So, Susie is starting this swim club and she decides she will add 2 new members. Each new member will ask 2 people each to become members. If every new member invites 2 people to become members, how many members will there be on the swim club at the end of month 4?
(How much wood could a woodchuck chuck if a woodchuck could chuck wood? Ahhhhh—)
Alright—some things need clarifying here. First off, how do we know the kids will actually get two members each to join? I mean, come on folks, this must involve big bucks for the parents and not every parent has the money OR the time to devote to a swim club just ‘cause lil’ ol’ Susie wants to have one. What a spoiled child! Why can’t she just join a swim club that already exists? If she’s that good a swimmer—but how do we know THIS?—if she is, then for heaven’s sake, she might be one of the best on an existing team and really help them out! Why, Susie could become a Olympic swimmer for all we know. Why start up one of your own when you could join one already in existence and maybe make something of yourself. But, OHHHHH NOOOO! Susie is determined to have her very own swim club.
Or is it more diabolical? Maybe Susie just wants to show off to her friends and their friends and their friends’ friends and their friends’ friends’ friends? Maybe she really IS that good. BUT…. Just a show off. I’ve known some Susie’s in my life, believe me, and……..well, that’s another story…………
On the other hand, maybe Susie doesn’t even know how to swim. In that case, who is going to teach her? How is she going to compete, anyway—who is in charge here? Now this involves parents getting/hiring someone to be the coach not to mention early-morning, late-afternoon after-school practices (and on Saturdays!) and getting the kids to and from practice on time and paying for all the training and getting the kids (on a bus, I suppose, which they’ll have to rent) to and from the meets—and who would be their competitors? I mean, this is getting expensive, people!
Okay, well, we don’t know the answer to the question yet, now, do we? Nope. We don’t’ know IF anybody even LIKES Susie and would JOIN her swim club, now do we?
But I digress……..
So on to the problem. I read it; Grandson read it; TMWLH read it. We decided that it was solved like this:
Month 1: We have the brat Susie plus she asks 2 new members and they agree to join. (We are assuming here she has 2 friends, anyway.)
So at the end of Month 1, there are 3 members—Susie and her two groupies.
Now, then, if each of the 3 members asks two people and they don’t go to their folks who veto the idea, then they join. So, then you have
Susie plus her two friends plus their six friends equals nine people on this team. (We’re already getting into the difficulty of deciding where they’re going to swim not to mention times to practice and carpooling and they’ve had to hire a coach and lifeguard…….. But never mind, on with the problem………)
So we have 9 people at the end of the second month.
The third month, everybody (after all, it’s a new swim team and they all really ARE new members—which begs another question, how long are the members ‘new members’? Is Susie a new member? How many friends does she have anyway?) asks two more friends. So we have 9 X 2 = 18 new people plus the original 9 from the end of month 2, so we have a total of 27 girls who have joined the team.
You see where this is leading, don’t you? Yep—too MANY girls already! I mean, somebody has to be a lifeguard every time they are in those pools, and now we have 27 of them, none of whom actually know HOW to swim and so you likely have to hire two lifeguards at least to keep them safe AND a coach. The parents are beginning to see this is pretty expensive.
At the end of the third month, you’ve got these 27 spoiled brats who each ask two more girls to join which is 27 X 2 = 54 plus the 27 you already had which makes 54 + 27 = 81
So by the beginning of the 4th month, you’ve got 81 girls all wanting to swim, in some gigantic pool which the parents now have to rent just for them—I mean, they might as well BUY a pool for heaven’s sake, with the cost factor in here.
You can carry it on out to month 4, but I don’t want to think about it………
Also, is the coach or are the coaches ‘members’ and if so do THEY have to ask for new members every month? Are they included in the total number of members? And what if a coach gets fed up with all these girls in a pool who can’t swim? And what if the coach quits, THEN what does lil’ ol’ Susie do? Not to mention the parents who are now fixing cookies and lemonade every day and carting that to the pools so the girls can have snacks—I mean, it’s becoming the focus of their lives. This is out of hand……
(I go to bed and think on it. The whole idea becomes ridiculous—surely this can’t be how the question should be answered? But then again, it is NOT HOW A QUESTION SHOULD BE ASKED! Too many unanswered questions about the problem to begin with! It’s way too ambiguous—)
So, as I am wont to do, I got up about 1:30 and rethought the entire problem. Like this:
We’ve got the previously established Susie, the Brat, who wants this swim team.
Her parents don’t like it, but think what the heck? I mean, she’ll never get THAT many kids on a team which she thought up herself, so they say alright……..Besides, lil’ Susie ain’t exactly the most popular kid in school and actually needs some friends, not to mention some type of activity to keep her out of their hair!
So, she gets two more girls on her team the first month, telling them they have to get two members each the next month. They agree for some reason.
End of month one, 3 members.
Each of the two new girls get two more girls each:
2 X 2 = 4 plus they have the original 3 which makes 7 members at the end of the second month.
The third month, each of the 4 new members from the second month get 2 girls to join (I don’t know what these girls were doing before this silly swim team came along, but I guess they didn’t have busy extracurricular activities going on, so they joined.) Anyway, now you have 4 X 2 = 8 plus the original number from the second month which was 7 so that makes 15 members on this team at the end of the third month.
Now, then it’s the fourth month and each of the 8 members who joined in month 3 have the fun of finding 2 more girls each to join, and somehow they do (this is a very dull place, wherever they live), so you’ve got 8 X 2 = 16 plus the total from the end of the third month which is 15, so 15 + 16 = 31 members.
Now, really, girls that is ENOUGH! I mean you’ve already committed half your parents’ incomes to this swimming business, hired a coach, hired a lifeguard, and you’ve got the audacity to schedule practice before school AND after school and on Saturdays, expecting treats all the time—who do you think is responsible for getting you to and from those practices and bringing all the cookies and lemonade?
Grandma and Grandpa.