Question

Justin is packing a container with books. The dimensions of each book are 8 inches by 6 inches by 2 inches. • The dimensions of the container are 16 inches by 12 inches by 12 inches. . All of the books and the container are rectangular prisms. Part A How many books can fit in the container if the books are packed so that there is no unused space in the container? Enter your response in the first response box. Part B Each book weighs 2 pounds. The maximum weight the container can hold is 40 pounds. What is the greatest number of books that can fit in the container without going over the container's weight limit? Enter your response in the second response box. ​

Answer 1

By finding the quotient between the volumes, we will see that 24 books can be fit on the container, and by weight, the container can hold 20 books.

How many books can be fitted on the container?

Remember that the volume of a rectangular prism of length L, width W, and height H is given by:

V = L*W*H

Then the volume of each book is:

V = 6in*2in*8in = 96 in^3

And the volume of the container is:

V' = 16in*12in*12in = 2,304 in^3

The number of books that fit in the container is given by:

N = V'/V = 2,304 in^3/96 in^3 = 24

How many books the container can hold?

Each book weighs 2 pounds, and the container can hold 40 pounds, then we need to solve the linear equation:

2*x = 40

To get the maximum number of books that the container can hold:

x = 40/2 = 20

x = 20

The container can hold a maximum of 20 books.

If you want to learn more about volumes, you can read:

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