Juan plans to build a bookcase to store his paperback books, DVDs, and CDs. He has lumber that he will use for the sides and back of the bookcase. The bookcase will have five shelves, and each shelf will be 2 1/2 feet.
DVD cases are 9 16 inch wide.
a. If Juan has 60 DVDs, how many of them will fit on one shelf?
b. How wide would a DVD case have to be in order for 60 of them to fit on one shelf? Give the answer in feet.
I now count 11 "Juan and his bookcase" questions.
I don't think Juan will ever get it build.
See the Related Questions below.
In order to answer these questions, we need to determine the width of the DVD cases and calculate how many of them will fit on one shelf.
a. To find out how many DVD cases will fit on one shelf, we need to first convert the dimensions of the shelf and the width of the DVD cases to a common unit.
The width of each shelf is given as 2 1/2 feet. To convert it to inches, we need to multiply it by 12 (1 ft = 12 inches):
2 1/2 feet * 12 inches/foot = 2.5 feet * 12 inches/foot = 30 inches.
The width of each DVD case is given as 9/16 inch.
Now, we need to divide the width of the shelf by the width of one DVD case to find out how many DVD cases will fit on one shelf:
30 inches / (9/16) inch = 30 inches * (16/9) = 53.33 (approximately).
Therefore, approximately 53 DVD cases will fit on one shelf.
b. To determine how wide a DVD case needs to be in order for 60 cases to fit on one shelf, we can reverse the calculation we just made.
We know that 53 DVD cases occupy 30 inches of width on the shelf. So, in order to find the width of one DVD case that will allow for 60 cases on the shelf, we can set up the following equation:
60 DVD cases * (width of one DVD case in inches) = 30 inches
Now, let's solve for the width of one DVD case:
(width of one DVD case in inches) = 30 inches / 60 DVD cases = 0.5 inches.
Converting this to feet, we divide by 12 (since 1 ft = 12 inches):
0.5 inches / 12 inches/foot = 0.0417 feet (approximately).
Therefore, a DVD case would need to be approximately 0.0417 feet wide in order for 60 of them to fit on one shelf.