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Pennies and Remainders

```Date: 01/13/2003 at 18:18:47
From: Kelsey
Subject: Pennies/word problems

Arnie has between 300 and 400 pennies in his collection. When he
divides them into groups of 4, 5, or 9 there is always one penny left
over. How many pennies does Arnie's collection contain?
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Date: 01/14/2003 at 10:33:13
From: Doctor Kastner
Subject: Re: Pennies/word problems

Hi Kelsey -

Let's think about an easier problem as a warmup.

Suppose Arnie has between 40 and 50 pennies and he finds that if he
divides them into groups of 3 or 7 he has one left over each time.
How many pennies does Arnie have?

The key here is to note that Arnie can ALMOST divide them into groups
of 3 and 7. This suggests that we should look for a number that is a
little more than a common multiple of 3 and 7. Well, 21 is a common
multiple since both 3 and 7 go into 21 with no remainder. But we want
a remainder of 1. So how about trying 22? That seems to work since 22
divided into groups of 7 gives 3 groups with one left over and 22
divided into groups of 3 gives 7 with one left over. Great! We are
done!

Oh...wait...he has between 40 and 50 pennies. Hmm...well, let's think
about another common multiple of 3 and 7...how about 42? 3 goes into
42 evenly, and so does 7. But again, we want to have one left over
each time, so let's add 1 to 42 which gives us 43. Does that work?
Yes, 43 divided into groups of 3 gives 12 with 1 left over, and 43
divided into groups of 7 gives 6 with 1 left over. Now we are done.

This is exactly the type of thing you need to do for your problem.

I hope this helps. Write back if you're still stuck, or if you have
other questions.

- Doctor Kastner, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
Elementary Word Problems