songsparrow Posted October 23, 2014 Share Posted October 23, 2014 This is the problem from Jacob's Geometry 2d ed, Chap 2 Lesson 2 Set III: A bookworm eats its way from page 1 of volume 1 to the last page of volume 20 of an encyclopedia. The books are arranged in order on a bookshelf in the normal way. If the inside of each volume is 4 cm thick and each cover is 0.2 cm thick, through what distance did the bookworm chew? Our answer: Each book is 4.4 cm thick (4 cm insides + two 0.2 cm covers). There are 20 volumes so 4.4 x 20 = 88 cm. But the bookworm did not eat the front cover of volume 1 or the back cover of volume 20, so 88 - 0.4 = 87.6 cm. The answer key says: Covers: 38 x 0.2 cm = 7.6 cm Insides: 18 x 4 cm = 72 cm Total: 7.6 + 72 = 79.6 cm The answer key also includes a drawing that shows that they did not include the pages of volume 1 or volume 20 in the calculation (thus only 18 insides). We think this is wrong as the question is written. We think this would be correct if the question read "A bookworm eats its way from the last page of volume 1 to the first page of volume 20." So, who is correct - us or the answer key? If we are incorrect, can you please explain why? Quote Link to comment Share on other sites More sharing options...
EKS Posted October 23, 2014 Share Posted October 23, 2014 I think you are correct. Quote Link to comment Share on other sites More sharing options...
lexi Posted October 23, 2014 Share Posted October 23, 2014 I think you are correct. I agree. But we are not in algebra yet so I might be missing something. Algebra is a distant memory for me.... Quote Link to comment Share on other sites More sharing options...
creekland Posted October 23, 2014 Share Posted October 23, 2014 I'd go with yours based upon the info you supplied. I'd also wonder how the bookworm got into the first page without eating from the top/bottom or through the cover, but that's just me... maybe it just ate a trail along the top? I suppose that could happen. Quote Link to comment Share on other sites More sharing options...
Critterfixer Posted October 23, 2014 Share Posted October 23, 2014 Actual book borers are rare and the chemical composition of modern paper is not very digestible for them... But that's my Calvin answer. :D Quote Link to comment Share on other sites More sharing options...
wendyroo Posted October 23, 2014 Share Posted October 23, 2014 This is the problem from Jacob's Geometry 2d ed, Chap 2 Lesson 2 Set III: A bookworm eats its way from page 1 of volume 1 to the last page of volume 20 of an encyclopedia. The books are arranged in order on a bookshelf in the normal way. If the inside of each volume is 4 cm thick and each cover is 0.2 cm thick, through what distance did the bookworm chew? It all comes down to the bolded. Hold up a book like it would go on a bookshelf. Where is page 1? On the right...not the left. The bookworm will not eat through the rest of the book. Wendy Quote Link to comment Share on other sites More sharing options...
Critterfixer Posted October 23, 2014 Share Posted October 23, 2014 That's rather nasty...but clever... Quote Link to comment Share on other sites More sharing options...
Cosmos Posted October 23, 2014 Share Posted October 23, 2014 It all comes down to the bolded. Hold up a book like it would go on a bookshelf. Where is page 1? On the right...not the left. The bookworm will not eat through the rest of the book. Wendy Oh, now that's just sneaky. I bet an engineer wrote this problem, not a mathematician. Quote Link to comment Share on other sites More sharing options...
EKS Posted October 23, 2014 Share Posted October 23, 2014 It all comes down to the bolded. Hold up a book like it would go on a bookshelf. Where is page 1? On the right...not the left. The bookworm will not eat through the rest of the book. Wendy See, this is why I shouldn't post anything when I first wake up! Quote Link to comment Share on other sites More sharing options...
creekland Posted October 23, 2014 Share Posted October 23, 2014 It all comes down to the bolded. Hold up a book like it would go on a bookshelf. Where is page 1? On the right...not the left. The bookworm will not eat through the rest of the book. Wendy VERY good point. I was envisioning opening the book and seeing the worm's destruction and going from there (esp with my rabbit trail thought). This is one case where IRL, the actual math would have been correct. It's only our thought process drawing the pic that was incorrect. Quote Link to comment Share on other sites More sharing options...
songsparrow Posted October 23, 2014 Author Share Posted October 23, 2014 Thank you Wendy. I completely missed that twist! Quote Link to comment Share on other sites More sharing options...
Alessandra Posted October 23, 2014 Share Posted October 23, 2014 It all comes down to the bolded. Hold up a book like it would go on a bookshelf. Where is page 1? On the right...not the left. The bookworm will not eat through the rest of the book. Wendy Agreeing with Wendy. For the first volume, the worm will miss the back cover and all the pages except for the first of volume 1 and miss the front cover and all the pages except the last one of volume 20. But I also think this is more of a logic/puzzle question than an algebra one, IMO. Tricky, unless you are accustomed to drawing representations of word problems. The Singapore Math bar method works beautifully with this kind of problem. Quote Link to comment Share on other sites More sharing options...
songsparrow Posted October 23, 2014 Author Share Posted October 23, 2014 It is more of a logic puzzle in this case. The Set III problems are bonus problems that extend the subject, introduce some sort of a twist or introduce some interesting application of the subject to real life. They're mostly for fun and to make you really stop and think! (edited to match up my cases!) Quote Link to comment Share on other sites More sharing options...
Mimm Posted October 23, 2014 Share Posted October 23, 2014 It all comes down to the bolded. Hold up a book like it would go on a bookshelf. Where is page 1? On the right...not the left. The bookworm will not eat through the rest of the book. Wendy Sneaky! :-) I would have pictured this wrong as well. Quote Link to comment Share on other sites More sharing options...
Alessandra Posted October 23, 2014 Share Posted October 23, 2014 It is more of a logic puzzle in this case. The Set III problems are a bonus problem that extends the subject, introduces some sort of a twist or introduces some interesting application of it to real life. They're mostly for fun and to make you really stop and think! Sounds fun, but thank goodness there is an answer key! Btw, I need the answer key for the first grade level of the Stepping Stones logic series, lol. Quote Link to comment Share on other sites More sharing options...
rdj2027 Posted October 23, 2014 Share Posted October 23, 2014 LOL, my son had the same problem in his AOPS Pre-algebra class. It was one of the few that stumped him, and my suggestion that maybe he should pay more attention to our bookshelves didn't go over very well :lol: Quote Link to comment Share on other sites More sharing options...
creekland Posted October 23, 2014 Share Posted October 23, 2014 The good thing about encountering a problem like this is that once you miss it once, you'll never miss it again. ;) Quote Link to comment Share on other sites More sharing options...
Alte Veste Academy Posted October 23, 2014 Share Posted October 23, 2014 This kind of problem is a perfect example of why I encourage my kids to doodle-work out their problems! :lol: Quote Link to comment Share on other sites More sharing options...
creekland Posted October 23, 2014 Share Posted October 23, 2014 This kind of problem is a perfect example of why I encourage my kids to doodle-work out their problems! :lol: Oh, I'd have drawn the problem. I just wouldn't have thought about which page was where when the books were on the shelves. I didn't even think about it when the OP mentioned the answer key having drawn it out the way it was. I probably should have thought about it... but, well, at least I can blame either the cold I have or the brain tumor. The bt should be good for excuses for the rest of my life! The rest of you who didn't think about it have to come up with your own excuses. :lol: I am glad this thread is here so if I ever encounter such a problem I won't forget about it in the future. :D Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted October 23, 2014 Share Posted October 23, 2014 So was I the only one who thought, "Oh no you need to deal with this book worm problem before more books get ruined!" Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted October 23, 2014 Share Posted October 23, 2014 The good thing about encountering a problem like this is that once you miss it once, you'll never miss it again. ;) A yup. I sometimes get so convinced I found an error that I'm ready to call up the publisher. I always hold off to think about the problem some more and then damn I realize I'm wrong. Thank goodness I didn't make an @$$ of myself. LOL Quote Link to comment Share on other sites More sharing options...
creekland Posted October 23, 2014 Share Posted October 23, 2014 A yup. I sometimes get so convinced I found an error that I'm ready to call up the publisher. I always hold off to think about the problem some more and then damn I realize I'm wrong. Thank goodness I didn't make an @$$ of myself. LOL I'm kind of used to finding errors - once in a while in books, more often in answer keys that are hand done. I always double or triple check things before confronting whoever made the error - just in case! With answer keys it's almost always one of those idiot error deals that we can all do. With books there's a bit more thought needed. Only once did I have my guy e-mail the writer - fortunately, we were correct that it WAS an error! (Phew!) Quote Link to comment Share on other sites More sharing options...
lexi Posted October 23, 2014 Share Posted October 23, 2014 Oh, now that's just sneaky. I bet an engineer wrote this problem, not a mathematician. I would have never figured this out.... Quote Link to comment Share on other sites More sharing options...
Guest andreea Posted October 24, 2014 Share Posted October 24, 2014 great answer wendy , and yes , it's a logic exercise. Quote Link to comment Share on other sites More sharing options...
Penguin Posted October 25, 2014 Share Posted October 25, 2014 What a great problem! I recently acquired a 2nd edition Jacobs Geometry & Soln Manual, and am very excited about the logic chapters in the beginning. No matter what Geometry text we end up choosing, DS and I will work through the logic chapters. Quote Link to comment Share on other sites More sharing options...
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