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Representing the Average

Date: 08/18/98 at 18:38:44
From: cleatus
Subject: Algebra 

I am totally stuck and don't know how to begin. Please help me with 
answering this question.

Suppose a, b, and c represent one student's scores on three math tests. 
Write an expression for the students' average if:

   a. all three tests count equally.
   b. the last counts as though it were two.

Date: 08/19/98 at 16:25:52
From: Doctor Peterson
Subject: Re: Algebra 

Hi, Cleatus. If you are familiar with averages, this shouldn't be too 
hard, but you are probably not used to writing expressions like this, 
and part b might be a little confusing. I'll try to lead you through 
it without actually writing down the answers.

First, remember what an average is: you add up the three scores, then 
divide by three. So for part a, just write an expression that adds up 
a, b, and c, then divides the result by 3.

Now in part b, you have to count the last test as two. So it's as if 
the student got scores of a, b, c, and c on four tests. Write an 
expression that adds these four numbers, then divides the sum by 4.

At the beginning, algebra is just a matter of learning to write out in 
symbols what you've been doing with numbers for years, so questions 
that sound hard may be easier if you try first using numbers instead 
of letters. If you have trouble, try rewriting the question in terms 
of numbers: if a student's scores are 90, 80, and 75, what is his 
average? what if the 75 counted as if it were two tests? Write out the 
answers without actually adding or dividing; then try doing the same 
thing with a, b, and c.

Write back if you need more help.

- Doctor Peterson, The Math Forum
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Associated Topics:
High School Statistics

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