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.
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.
You only have 30 of the bigger boxes...
Therefore
combined, you want to pack at least 180 of the pairs
of shoes.
So the system of equations is
Here is the graph:
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:
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
