Expert: Josh - 7/13/2007

Question
1.   Solve the equation abx = cy  for each of the following:

a.   the variable x

Answer:


Show your work:



  b.   the variable a
  
Answer:


Show your work:


  


c.   the variable c
  
Answer:


Show your work:






2.   Solve the equation ay/x = cz  for each of the following:

  a.   the variable y
  
Answer:


Show your work:


  b.   the variable z
  
Answer:


Show your work:


  c.   the variable x
  
Answer:


Show your work


Answer
Aaron,

You need to try this yourself to gain any benefit from it. Ultimately, you will be the person sitting for the exam, not me. If you don't know how to go about doing this, or if you don't see the point of the question, then please ask.

The goal here is to separate a variable (unknown quantity) from the rest of the equation.

o What are we allowed to do?
In order to make a variable say "a" the subject of an equation, we carry out addition (or subtraction) and/or multiplication (or division) simultaneously on both sides of the equation.

e.g., For abx = cy, each variable "a","b","c","x" and "y" represent some unknown quantity (think of this as some mystery number). The equation simply shows how these variables are related.

In Q1b, to make "a" the subject (leaving it on the LHS of the equation), we divide both sides by bx to get a=(cy)/(bx). Note: In algebra, when we write "bx", we mean "b" multiplied by "x".

Have a go at the other parts yourself.

In Q2, we have ay/x=cz. In part c, to make x the subject, we do this in two steps.

Step 1: multiply both sides by x
(ay)/x = cz   becomes (ay) = czx
Step 2: divide both sides by cz,
we get (ay)/cz = x. Usually, we write this as x=ay/cz.

Another way to do this is to invert both sides of the equation. From (ay)/x = cz to x/(ay) = 1/(cz). Then, multiply both sides by "ay" to obtain x=(ay)/(cz).