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Unitary Method Problem

Date: 02/01/99 at 19:13:36
From: Tamara
Subject: A Unitary Method Problem

Runts come in a carton. There are 8 packages in one carton. There are 
3 boxes in each package. If there are 170 runts in one box, how many 
runts are there in 6 cartons?

Date: 03/01/99 at 17:48:36
From: Doctor Swiss
Subject: Re: A Unitary Method Problem

This can be a difficult question to take in all at once. The best way 
to approach it is to break it down into steps. The first step is to 
notice how runts, boxes, packages, and cartons are related. It might 
help to draw a diagram, like this one:

 170 runts/box --> 3 boxes/package --> 8 packages/carton --> 6 cartons

Just so you know, by runt/box, we mean runts in a box. Now you can see 
how everything is related, and you can also see the steps that you have 
to take. Now to find out the number of runts in 6 cartons, it would 
help us to see how many packages are in 6 cartons. Why? Well, once we 
know the number of packages in 6 cartons, we can find out the number of 
boxes in 6 cartons, and finally the number of runts in 6 cartons. 

So now we are trying to find the number of packages in 6 cartons. We 
know the number of packages on 1 carton is 8. What if we had 2 cartons? 
Then we would have 8 cartons from the first package and 8 from the 
second, for a total of 8 + 8 = 16. Note that this is also 8 * 2 = 16 
cartons. Try this for 3 cartons. I hope you can see the jump and figure 
out that there are 8 * 6 packages in 6 cartons. You can repeat this 
process to find that there are 3 * 8 * 6 boxes in 6 cartons. You need 
one more step to find the number of runts in 6 cartons.

It turns out that this problem is just one big multiplication problem. 
Please write back if you need more help or have any more questions. 
Good luck, 

- Doctors Swiss, Teeple, and Stacey, The Math Forum   
Associated Topics:
Middle School Word Problems

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