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

so P equals three.  That's your answer.  
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/