Question 1068131
You are packing pairs of boxed shoes into bigger boxes for 
shipping. You can either fit 6 adult shoe boxes or 9 children’s 
shoe boxes into the bigger box. You only have 30 of the bigger 
boxes and, combined, you want to pack at least 180 of the pairs 
of shoes. Write a system of inequalities to model this situation. 
Then graph the system. Give 2 sample solutions.<pre><b><font size=4>
Let x = the number of bigger boxes that will contain 6 adult shoe
boxes.
Let y = the number of bigger boxes that will contain 9 children's
shoe boxes.
</pre>You only have 30 of the bigger boxes...</pre>
Therefore
{{{x + y <=30}}}
</pre>combined, you want to pack at least 180 of the pairs 
of shoes.<pre>
{{{6x+9y>=180}}}
So the system of equations is
{{{system(x + y <=30,6x+9y>=180)}}}

Here is the graph:

{{{drawing(600,600,-1.3,32.6,-1.3,32.6,
graph(600,600,-1.3,32.6,-1.3,32.6,50,y>30-x),
graph(600,600,-1.3,32.6,-1.3,32.6,50,y<(180-6x)/9),
graph(600,600,-1.3,32.6,-1.3,32.6),


graph(600,600,-1.3,32.6,-1.3,32.6), line(30,0,0,30),line(30,0,0,20) )}}}

The feasible region is the white area.  To find 2 sample solutions, we
pick 2 points either IN, or ON the boundary of, the white region.

Say we pick the point (5,22) which is in the white region, and (9,14)
which is ON the boundary of the white region:

{{{drawing(600,600,-1.3,32.6,-1.3,32.6,
graph(600,600,-1.3,32.6,-1.3,32.6,50,y>30-x),
graph(600,600,-1.3,32.6,-1.3,32.6,50,y<(180-6x)/9),
graph(600,600,-1.3,32.6,-1.3,32.6),
locate(5,22,"(5,22)"), locate(9,15,"(9,14)"),
circle(5,22,.2),circle(9,14,.2),
graph(600,600,-1.3,32.6,-1.3,32.6), line(30,0,0,30),line(30,0,0,20) )}}}

The two sample solutions are 
1. 5 big boxes containing 6 adult shoe boxes each, and 22 big boxes
   each containing 9 children's shoe boxes each.  That's 5*6+22*9 = 228 
   shoe boxes.

1. 9 big boxes containing 6 adult shoe boxes each, and 14 big boxes
   each containing 9 children's shoe boxes each.  That's 9*6+14*9 = 180 
   shoe boxes.
Edwin</pre></b></font>