Find the Number

Date: 05/14/97 at 16:04:13
From: Erin Warner
Subject: Number Word Problems (algebraic phrases and equality)

Five times a certain number is six less than three times the same 
number.  What is the number?

Date: 05/20/97 at 10:28:33
From: Doctor Edwards
Subject: Re: Number Word Problems (algebraic phrases and equality)

Erin,

First I'll show you how to solve similar problems, and then you can 
try to use the same method on yours.

Example 1: 4 times a certain number is 8.  What is the number?

Let's rewrite this as a math equation.  In place of "a certain 
number," I'll use a variable, X.  X can be anything, but in this case 
it will be the answer I'm looking for. Now I can translate the words 
in the problem into:

      4 * X = 8

To find out what X is, I need to undo everything that is being done to 
it. In this example, it is being multiplied by 4.  When I divide by 
four, I have to be careful because I have to divide the things on each 
side of the "=".  I can change my equation to:

    4 * X      8
   -------- = --- 
      4        4

Then to:

          X = 2

Now I have my answer: the number is 2.

Example 2: 4 times a certain number is 9 more than the same number.  
What is the number?

This time, my equation will be different:
                        
     4 * X = X + 9

This problem is harder because I have an X on each side of the 
equation and I need them to be on the same side. If I subtract an X 
from both sides, the right side will become 9, and, since I am 
subtracting one X from 4 X's on the left, it becomes 3 X's, or 3 * X.  
Now my equation is:

     3 * X = 9

Now this problem is very similar to the first one.  I will divide both 
sides by 3, to get X = 3.

To solve your problem you need to come up with an equation, with X 
representing the number you don't know.  Then you need to try to 
change the equation so that X is alone on one side of the "=" and a 
number is alone on the other side.  That number will be the answer.  

One last hint: think of '5 * X' as 5 X's and '3 * X' as 3 X's.

If you need more help, write in again. 

-Doctor Edwards,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/