Question

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.

Answer 1

Answer:

x + y <= 30

6x + 9y >= 180

Step-by-step explanation:

If we call x the number of big boxes containing six smaller boxes of adults shoe and y the number of big boxes containing nine smaller boxes of children's shoe:

x + y <= 30 -> we only have 30 big boxes

 

We only want to pack 180 pairs of shoes, so we want the number of pairs of shoes in x and y to be less than 180, therefore:

6x + 9y >= 180

In the graph down below see that any selection of x and y inside the purple region satisfies the system of inequalities and is a solution to the problem.  

Answer 2

Answer:

Step-by-step explanation:

Let call

x number of adult shoe boxes, and

y number of children shoe boxes

And constraints  

1.-We have to pack at least 180 pairs of shoes then

x + y ≥ 180

2.- We have only 30 bigger boxes and can pack either 6 adult boxes or 9 children boxes

Then

6x + 9y ≤ 30

Graphing ( see annex  c)

x + y ≥ 180                     y ≥ -x + 180             negative slope (-1)

                                                                  y axis interception  180

6x + 9y ≤ 30  

9y ≤ 30 - 6x                          negative slope ( - 2/3 )                

y ≤ - 6/9*x + 30/9                   y axis interception 30/9