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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?
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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/
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Associated Topics:
Middle School Algebra

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