Challenging Word Problems 5 problem

[Guest DianeinNM]

In the first section, question 20, my dd and I can't figure this out:

 

5 books and 9 magazines are $156

9 books and 5 magazines are $180

How much more is a book than a magazine?

 

The difference is $24

14 books and 14 magazines would be $336

Drawing bars, we see that 4 books vs. 4 magazines has a difference of $24

One book and one magazine = $336/14 = 24

 

It seem clear that we're floundering around, doesn't it?

 

Thanks for any help!

 

:-) Diane

[HootyTooty]

http://www.welltrainedmind.com/forums/showthread.php?t=105707

[daybreaking]

In the first section, question 20, my dd and I can't figure this out:

 

5 books and 9 magazines are $156

9 books and 5 magazines are $180

How much more is a book than a magazine?

 

The difference is $24

14 books and 14 magazines would be $336

Drawing bars, we see that 4 books vs. 4 magazines has a difference of $24

One book and one magazine = $336/14 = 24

 

It seem clear that we're floundering around, doesn't it?

 

Thanks for any help!

 

:-) Diane

 

I'm not sure if this is the "Singapore" way, but from what you did above, I would look at the first equation and break it apart into 5 books + 5 magazines + 4 magazines = $156. Then, you have 5 sets of 1 book + 1 magazine, which would be 5 x 24 or $120. The remaining 4 magazines would then be $156-$120 or $36, so each would be $9. Lastly, that could be used to find the price of a book from either equation. Using the second, one would have 9 books + 5 magazines @ $9 each = $180. $180 - $45 = $135 left for the 9 books, so by dividing, each would be $15.

[ChandlerMom]

In the first section, question 20, my dd and I can't figure this out:

 

5 books and 9 magazines are $156

9 books and 5 magazines are $180

How much more is a book than a magazine?

 

The difference is $24

14 books and 14 magazines would be $336

Drawing bars, we see that 4 books vs. 4 magazines has a difference of $24

One book and one magazine = $336/14 = 24

 

It seem clear that we're floundering around, doesn't it?

 

Thanks for any help!

 

:-) Diane

 

Actually, I think you're doing fine. Since the question is how much more each book is and off the bat you saw that 4 books costs $24 more than 4 magazines, EACH book must cost 24/4=$6 more than each magazine. DONE. [Once you have achieved a 1:1 comparison of the two items, you've found the per item difference.]

 

If the question was how much each cost, you could then go to your last equation (one book and magazine cost $24) and since a book costs $6 MORE, if you bought 2 books instead it would cost $24 + $6 = $30, so each book would be $15. Each magazine would be $6 less, so $9.

 

Always good habit to plug that back into the original equations to check your answers and you'll see:

5x15 + 4x9 = 136 and 4*15 + 5*9 = 180

 

I think the key is to always underline (or focus on) what the question is asking for, and at each step ask "so, what is this telling me?" and "Does this get me closer to the answer for my original question?"

[Candid]

Here's a post over on their forum:

http://www.singaporemaths.com/forums/showthread.php?335-CWP5-p.10-20&highlight=magazines

 

I reject the idea that there is some special "Singapore way." They actually teach a lot of things to help students break down word problems and you'll see that several are offered in the thread attached.