How Many Boxes? A Diagram

Date: 03/20/2003 at 07:45:18
From: Janet
Subject: Fractions

There were juice boxes in a cooler. Jared took 1/6 of them. Sara took 
1/4 of what was left. Now there are 15 boxes. How many boxes were 
there to start with?

Date: 03/20/2003 at 23:24:59
From: Doctor Ian
Subject: Re: Fractions

Hi Janet,

I'd solve this by working backward. At the end, you have 15 boxes:

  * * * * *
  * * * * *
  * * * * *

Now, before this, I had more:

  * * * * *
  * * * * *  +  ?
  * * * * *

How many more? Well, my friend took 1/4 of what I had. So for each 4
that I had, he took 1, and left me with 3. So for each 3 that I have,
I must have had 1 more!  

Does that make sense? So I can add one to each column of three in my 
picture:

  * * * * *
  * * * * * 
  * * * * *
  $ $ $ $ $

Now I'm in sort of the same boat. Before this, I had more:

  * * * * *
  * * * * *  +  ? 
  * * * * *
  $ $ $ $ $

How many more? Well, my friend took 1/6 of what I had. So for each 6
that I had, he took 1, and left me with 5. So for each 5 that I have,
I must have had 1 more.  

Can you see how you'd adjust the picture to add the missing items?  

Note that once you've done this step, your picture shows you how many
items you must have started with. 

Does this help?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/