Ratio of Greek to Latin Exams

Date: 06/10/2003 at 18:57:36
From: Steve
Subject: Ratio of a number

Susanna took several examinations in Greek and Latin.  Her average 
score that is, the arithmetic mean, on all the exams was 88. Her 
average on the Greek exams alone was 80, and her average score on 
Latin exams alone was 92. What is the ratio of the number of Greek 
exams to the number of Latin exams?

Date: 06/10/2003 at 22:25:08
From: Doctor Ian
Subject: Re: Ratio of a number

Hi Steve,

This _is_ a tricky question, isn't it?

Let's say that the number of Greek exams is G, and the number of Latin
exams is L. (We could use 'x' and 'y', but it's easier to keep things
straight with names that reflect what they mean.) 

Susanna's mean score for all the exams would be

       G*(mean for Greek only) + L*(mean for Latin only)
  88 = -------------------------------------------------
                              G+L

(Do you see why this is the case?)

We're told the means for the separate subjects, so we can substitute
those into the equation to get

       G*80 + L*92
  88 = -----------
           G+L

Now, this isn't enough information to solve for either L or G, but the
idea is to work with this equation until you get something that
looks like 

  G
  - = [some expression without G or L in it]
  L

Does this make sense?  Is it enough to get started?

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