Solving a Ratio Problem

Date: 02/06/2006 at 20:21:39
From: Jennifer
Subject: How do you solve a ratio?

There are 33 red and yellow counters in a container.  The ratio of red 
to yellow is 3 to 8.  How many red and yellow counters are there?

I know there are 33 and that for every three red there are eight 
yellow.

Date: 02/06/2006 at 22:08:44
From: Doctor George
Subject: Re: How do you solve a ratio?

Hi Jennifer,

Thanks for writing to Doctor Math.  I'll show you two ways to think
about this problem, one using algebra and one without it.

One of my high school teachers showed me a clever way to solve this
problem using algebra.  If we use R and Y for the number of red and
yellow counters then let

   R = 3x
   Y = 8x

for some unknown value x.  We can see immediately that R/Y has the
correct ratio of 3/8.

Now find the sum.

   R + Y = 33

Can you finish it from here?  When you take the next step you should
see the reason for introducing the new variable x.

Another way to think about this, which is very similar but doesn't use
the variable, is to think about groups of the counters.  You know that
for every 3 red there are 8 yellow, so together that would make a
group of 11 counters.  How many of those groups of 11 are there if
there are 33 counters in the container?  Can you use that information
to figure out how many of each color there are? 

Write again if you need more help.

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