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### Finding Multiplier of Constants

```
Date: 8/5/96 at 13:29:19
From: SunjayMishra
Subject: Finding Multiplier of Constants

Hello!

This is an equation that I saw in a SAT book that I did not
understand:

X = a^2/b^2c

If n = 1/3x, then n is the value that results when the positive
numbers a,b,c in the expression above are each multiplied by which of
the following:

a) 1/9
b) 1/3
c) 3
d) 9
e) 27

I would also appreciate it if you could e-mail me some educational
sites, such as an Internet public library, that are free to use.

Thanks for the help!
```

```
Date: 8/5/96 at 17:29:6
From: Doctor Paul
Subject: Re: Finding Multiplier of Constants

Okay... here's the idea.  You want to multiply a, b, and c by some
number and then have that return X/3 after you simplify it out.

Let's do it:

I'm going to call the number we are looking for 'P'

X      (a*P)^2
--- = ---------------
3     (b*P)^2 * (c*P)

X       a^2 * P^2
--- = ------------------
3       b^2 * P^3 * c

X       a^2
--- = ----------
3    P * b^2 * c

Now we make a substitution:

let's look at something that was given in the definition:

a^2
X = --------
b^2*c

plug that into the right side of our equation:

X      X
--- =  ---
3      P

It corresponds with letter 'C'

>I would also appreciate it if you could e-mail me some educational
>sites, such as an internet public library, that are free to use.

Why not try doing a net search for public libraries? Go here:

http://search.yahoo.com/bin/search?p=public+libraries

I hope this answers your SAT question.  If you have any more, feel
free to send them to us.

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

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