How do I solve?

Question

A company sells boxes that are 2 3/8 feet high, 3 5/8 feet long, and 1 7/8 feet wide. John has a storage room that is 8 feet wide, 10 feet deep, and 12 feet high. You may rotate the boxes so that the width and length are interchanged, but the boxes may not be laid on their sides. a. What is the maximum number of boxes that he may stack on top of one another? b. How much room will there be left between the top of the stack of boxes and the ceiling?

Answer 1

From the problem statement and questions asked, your only concern is the height of each box as related to the inside storage room, regardless of how the boxes are rearranged by width and length. 

 

Let n = number of boxes stacked on the vertical

      h = height of each box = 2 3/8 ft

      H = length of storage room = 12 ft

 

Since the boxes have to be stored upright (they cannot be laid on their sides) then the maximum number of boxes that can be stacked (on the vertical),

n*h = H         or        n = H/h = 12 ft/(2 3/8 ft) = 5.05 boxes

 

Therefore, round down to a) 5 boxes is maximum number that can be stacked

 

and multiply by each box height to obtain total height of stacked boxes in storage room. 

 

5 boxes x (2 3/8 ft)/box = 11.875 ft

 

Now check the available space above the top box by solving for the difference in heights,

 

b) vertical gap = 12 ft - 11.875 ft = 0.125 ft    or    0.125 ft x 12 in/ft = 1.5 inches from top box to inside storage room ceiling