99 ’s family is using a shipping trailer that is 5 feet tall, 4 feet wide, and 12 feet long to load boxes of apples in. each box the apples are packed in has to have a volume of 5184 in3. design a box that will fill the trailer with no wasted space, and meet the volume requirements. show work

A cubic foot has a volume of (12 in)³ = 1728 in³. Your apple box is required to have a volume of (5184 in³)/(1728 in³/ft³) = 3 ft³.

The shipping trailer dimensions are not multiples of 3 ft, except in the length direction. The easiest box to design is one that is 1 ft square and 3 ft long.

For there to be no wasted space, the number of boxes must be ...

... (5 ft)·(4 ft)·(12 ft)/(3 ft³/box) = 240/3 boxes = 80 boxes.

In order to pack the trailer with no wasted space, there must be an integral number of boxes in each direction. There are 43 sets of dimensions that will give a 3 ft³ box that will pack the trailer. The one that has dimensions closest to a cube is

... 24 in wide × 15 in high × 14.4 in deep.

10 of these boxes can be put in the length of the trailer, and they can be stacked 2 wide and 4 high.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.