Georgia Posted July 29, 2011 Share Posted July 29, 2011 (edited) Yikes! I'm stuck on these type of problems!!! We're ok with others, but these particular ones have me stumped. We're trying to do this WITHOUT using algebra (since I don't think it's covered in level 5). Here's the problem from the book: 5 books and 9 magazines cost $156 altogether. 9 books and 5 magazines cost $180 altogether. How much more does each book cost than each magazine? We drew the following bar diagram: 5M 9M 24 = 156 ---- --------- ---- 9B 5M = 180 --------- --------- Can anyone explain the strategy for this type of problem? Thank you! Georgia ETA: Bar diagram should look like the typical kind - my symbols are not translating well Edited July 29, 2011 by Georgia extra information Quote Link to comment Share on other sites More sharing options...
Meredith Posted July 29, 2011 Share Posted July 29, 2011 These CWP always trip me up also. Are you using CWP 5 old edition or new edition. What page and number is this problem? Is the answer 12? I don't know if that is right or not and I'm not sure I can explain it even if it is, but I'll try. I usually go to http://www.singaporemaths.com/forums/forum.php when I am stuck on a CWP problem! It helps a lot! Quote Link to comment Share on other sites More sharing options...
Meredith Posted July 29, 2011 Share Posted July 29, 2011 OK, now I think the answer is 3. Oh brother! Maybe someone else should take over! :-) LOL! Quote Link to comment Share on other sites More sharing options...
regentrude Posted July 29, 2011 Share Posted July 29, 2011 Here's the problem from the book: 5 books and 9 magazines cost $156 altogether. 9 books and 5 magazines cost $180 altogether. How much more does each book cost than each magazine? I am not familiar with the bar graph method - but here is how I solved it without explicit algebra: If you look at the numbers, you will notice the symmetry: 9 and 5, 5 and 9. So, if you count everything together, you know that 14 books and 14 magazines cost 156+180=336. So one book and one magazine together cost 24. That means that 5 books and 5 magazines cost 5*24=120 In order to make 5 books and 9 magzines cost 156, the 4 extra magazines must cost 36. So, one magazine costs 9. If a book and a magazint together are 24, a book must cost 15, 6 more than a magazine. (To check: in order to make 9 books and 5 magazines be 180, 4 books must be 180-120=60, so yes, 15 for each book) Quote Link to comment Share on other sites More sharing options...
Georgia Posted July 30, 2011 Author Share Posted July 30, 2011 Thanks, Meredith! I have the 2006 edition, page 10, #20. The answer is $6. Quote Link to comment Share on other sites More sharing options...
Georgia Posted July 30, 2011 Author Share Posted July 30, 2011 Regentrude, thank you so much! That's a very clear explanation. I had gotten to the 1B+1M=$24. I'll be going back over your solution to see if I can relate it at all to a bar diagram. It may be that this is not terribly conducive to the bar diagram approach. Thanks for the help! Georgia Quote Link to comment Share on other sites More sharing options...
karensk Posted July 30, 2011 Share Posted July 30, 2011 Yikes! I'm stuck on these type of problems!!! We're ok with others, but these particular ones have me stumped. We're trying to do this WITHOUT using algebra (since I don't think it's covered in level 5). Here's the problem from the book: 5 books and 9 magazines cost $156 altogether. 9 books and 5 magazines cost $180 altogether. How much more does each book cost than each magazine? We drew the following bar diagram: 5M 9M 24 = 156 ---- --------- ---- 9B 5M = 180 --------- --------- Can anyone explain the strategy for this type of problem? (haven't read all the other posts) The two arrangements have something in common: at least 5 books and at least 5 magazines. Set up both bar diagrams with a segment for the 5 books and a segment for the 5 magazines on the left, to coordinate them: BBBBBMMMMM MMMM = 156 BBBBBMMMMM BBBB = 180 (When drawing the bar diagrams, I'd make the second arrangement have a longer bar, since its amount of 180 is greater than 156; difficult to show here.) Looking at the above, we realize since that the second arrangement (with the extra BBBB) costs more than the first arrangement (with the extra MMMM), then the BBBB must cost more than the MMMM (since the first parts of the two bar diagrams are identical: BBBBBMMMMM). So, the difference between the BBBB and MMMM is 180-156, which is 24. Since there are exactly 4 B's and 4 M's, we can divide 24 by 4 to arrive at the difference between one B and one M, which is 6. I hope that's right! Quote Link to comment Share on other sites More sharing options...
Georgia Posted July 30, 2011 Author Share Posted July 30, 2011 Karen, that makes sense! I see how you arranged the bar diagram to group the leftovers, and it's easier to "see" them. I still think this is a challenging type of problem! Thank you everyone! Quote Link to comment Share on other sites More sharing options...
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