Help with a Challenging Word Problem

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I have been racking my brain out for two days. :banghead:I have a feeling that it is simple and I am missing it. Can anyone help me?

Here's the problem:

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?

Does anyone have an idea how I can use a bar diagram or is it a ratio? I am stuck.

Thank you all!

Sincerely,

Karen

http://www.homeschoolblogger.com/testimony

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I'm too tired to do the math, but if you isolate one of the equations to solve for B or M, then plug it into the other equation, I think you should be able to solve it...

5b+9m=156

9b+5m=180

(1) isolate the second equation to solve for b:

9b+5m=180

9b=180-5m

b=(180-5m)/9

(2) then plug the equivalent of "b" into first equation to solve for m:

5b+9m=156

5[(180-5m)/9]+9m=156

(3) Then solve for m...

I could be off, but that is how I would start to attempt it. I wonder if there is a simpler way? Surely there has to be...

Edited by babysparkler
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I assume this is from Singapore CWP and you're supposed to solve w/o algebra. Each book cost \$6 more than each magazine. Here's how:

Set 1, \$156, has 5 pair of books and magazines, plus 4 extra magazines, for \$156.

Set 2, \$180, has 5 pair of books and magazines, plus 4 books, for \$180.

Set 2, with its 4 books instead of 4 magazines, costs \$24 more than Set 1. Ergo, each books costs \$6 more than each magazine.

Use bar diagrams to show the matching of the "pairs" of books and magazines. 'Fraid that I have no idea how to show that accurately in this format.

Terri

Edited by plansrme
Subtraction error
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That is MUCH easier than using the algebra ;)

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It is from Singapore Math CWP 5. It is problem #20. So, yes it needs to be solved without algebra.

Sorry.:tongue_smilie:

Sincerely,

Karen

http://www.homeschoolblogger.com/testimony

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That is MUCH easier than using the algebra ;)

After Singapore 6 (and I don't think this is from 6, maybe 4), my daughter thought Algebra I was a breeze. She's in Alg. II now and still thinks Singapore 6 was the hardest math she's ever done.

Terri

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I remember that problem and it has been three years!!!!!!

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I just did it in my head to see if I could figure it out. Can someone tell me if the books cost \$15 each and the magazines cost \$9 each?

I have no idea how I figured it out. DH always tells me that I have a weird way of looking at math, and my "non-methods" make no sense at all.

Cat

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I had a friend explain the bar diagram.

It is :

[/][/][/][/][/] books [][][][][/][/][/][/][/] magazines=\$156

[/][/][/][/][/][][][][] books [/][/][/][/][/] magazines=\$180

I crossed out 5 magazines to 9 magazines. I crossed out 5 books to 9 magazines. I am left with 4 books and 4 magazines. 180-156=24

\$24/4=\$6

It was simple. My son orginally got this answer and then erased it thinking it was wrong. I need a bar diagram.

Thanks to everyone who help me solve it.

Blessings,

Karen

http://www.homeschoolblogger.com/testimony

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