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### Representing the Average

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

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
thing with a, b, and c.

Write back if you need more help.

- Doctor Peterson, The Math Forum
Check out our web site! http://mathforum.org/dr.math/
```
Associated Topics:
High School Statistics

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