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### Marble Collection Fraction Problem

```
Date: 9/9/96 at 21:30:53
From: Anonymous
Subject: Tim and Danny's Marbles - Fraction Problem

3/4 of Tim's marble collection is the same size as 3/5 of Danny's
collection.  If they have 180 marbles altogether, how many marbles
must Danny give to Tim so that they will have the same number of
marbles?

Thanks,
Melissa
```

```
Date: 9/11/96 at 12:15:6
From: Doctor Ana
Subject: Re: Tim and Danny's Marbles - Fraction Problem

This is definitely an algebra problem. I'm going to set it up and let
you solve it.  Feel free to write back if you need help doing the
algebra.

First of all, let's call the number of marbles that Tim has x. We
could call Danny's marbles x if we wanted to, it doesn't matter, but
I'm going to call Tim's marbles x. We know that there are 180 marbles
between the two of them, so we know that Danny will have 180 - x
marbles.

Now we can set up the equation. 3/4 of Tim's marbles is the same as
3/4 * x, and 3/5 of Danny's marbles is the same as 3/5 * (180-x).
So our equation is:

3/4 * x = 3/5 * (180 - x)

To finish this problem, you can solve this equation for x, and that
will tell you how many marbles Tim has. Then it will be easy to find
out how many marbles Danny has, and from this you can figure out how
many marbles Danny should give to Tim.

-Doctor Ana,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Word Problems

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