<PRE><B>Question 106425</B>
From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be creative. Do not use word problems that are in the assignments or course material. 
&lt;pre&gt;
&lt;font face = &quot;symbol&quot;&gt;&amp;#233;&lt;font face = &quot;courier new&quot;&gt;1  1  1&lt;/font&gt;&amp;#249; &amp;#233;&lt;font face = &quot;courier new&quot;&gt;x&lt;/font&gt;&amp;#249; &lt;font face = &quot;courier new&quot;&gt;  &lt;/font&gt; &amp;#233;&lt;font face = &quot;courier new&quot;&gt;100&lt;/font&gt;&amp;#249;
&amp;#234;&lt;font face = &quot;courier new&quot;&gt;5 -3  0&lt;/font&gt;&amp;#250; &amp;#234;&lt;font face = &quot;courier new&quot;&gt;y&lt;/font&gt;&amp;#250;&lt;font face = &quot;courier new&quot;&gt; = &lt;/font&gt;&amp;#234;&lt;font face = &quot;courier new&quot;&gt; 10&lt;/font&gt;&amp;#250;
&amp;#235;&lt;font face = &quot;courier new&quot;&gt;0  3  4&lt;/font&gt;&amp;#251; &amp;#235;&lt;font face = &quot;courier new&quot;&gt;z&lt;/font&gt;&amp;#251;&lt;font face = &quot;courier new&quot;&gt;  &lt;/font&gt;  &amp;#235;&lt;font face = &quot;courier new&quot;&gt;290&lt;/font&gt;&amp;#251; 
&lt;font face = &quot;courier new&quot; size = 4&gt;&lt;b&gt;
The system of equations is

1x + 1y + 1z = 100
5x - 3y + 0z =  10
0x + 3y + 4z = 290

or

 x +  y +  z = 100
5x - 3y      =  10
     3y + 4z = 290

John has three numbers written on a sheet of paper.  He observes
that their sum is 100. He then observes that the difference 
between five times the first number and three times the second 
number is 10. Finally he observes that three times the second 
number increased by four times the third number is 290.  What 
three numbers are written on John&#39;s piece of paper?

Answer: first number = 20, second number = 30, third number = 50.

Edwin&lt;/pre&gt;</PRE>