Help with a Challenging Word Problem

[Testimony]

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

[babysparkler]

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 June 4, 2009 by babysparkler

[plansrme]

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 June 4, 2009 by plansrme
Subtraction error

[babysparkler]

That is MUCH easier than using the algebra ;)

[Testimony]

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

[plansrme]

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

[debbielong]

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

[Catwoman]

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

[Testimony]

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