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 long
. 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 assume you meant that each shelf is 2 1/2 feet long. Learn to type fractions.
If each DVD case is 9/16 in wide, then
30 รท 9/16 = 30 * 16/9 = 53.3
So, 53 will fit on a shelf.
Now for 60, just multiply 60 * 9/16 = ___ inches
convert to feet.
a. To find out how many DVDs will fit on one shelf, we need to calculate the total width of the DVDs and divide it by the width of each shelf.
Each DVD case is 9/16 inch wide.
To convert this to feet, we divide by 12 (since there are 12 inches in a foot):
9/16 inch = (9/16) / 12 feet = 9/192 feet = 3/64 feet.
Each shelf is 2 1/2 feet long.
To calculate the number of DVDs that will fit on one shelf, we divide the length of the shelf by the width of each DVD case:
(2 1/2 feet) / (3/64 feet) = (5/2) / (3/64) = (5/2) * (64/3) = (5 * 64) / (2 * 3) = 320/6 = 53 1/3.
Therefore, Juan will be able to fit approximately 53 DVDs on one shelf.
b. To find out how wide the DVD case would have to be in order for 60 of them to fit on one shelf, we divide the total width required by the number of DVDs:
Total width required = (60 DVDs) * (3/64 feet/DVD) = (60 * 3/64) feet = 9/64 feet.
Therefore, the DVD case would have to be 9/64 feet wide in order for 60 of them to fit on one shelf.
To find the number of DVDs that will fit on one shelf, we need to determine how many DVD case widths can fit within the length of the shelf.
a. To calculate the number of DVDs that will fit on one shelf, we need to convert the length of the shelf and the width of the DVD case to the same unit.
The length of the shelf is given as 2 1/2 feet. We can convert this to inches since the width of the DVD case is given in inches.
1 foot is equal to 12 inches, so 2 1/2 feet can be converted to:
2 1/2 feet = 2 * 12 inches + 1/2 * 12 inches = 24 + 6 inches = 30 inches
Now that we have the length of the shelf in inches, we can proceed to calculate the number of DVDs that will fit on one shelf.
Given that the width of the DVD case is 9/16 inch, we can divide the length of the shelf by the width of the DVD case to find the number of DVDs that will fit:
Number of DVDs = Length of Shelf / Width of DVD case
Number of DVDs = 30 inches / (9/16) inches
To divide by a fraction, we can multiply by the reciprocal (flip the fraction):
Number of DVDs = 30 inches * (16/9)
Simplifying:
Number of DVDs = 480/9 = 53.33
Therefore, approximately 53 DVDs will fit on one shelf.
b. To find the width a DVD case should be in order for 60 of them to fit on one shelf, we can rearrange the formula we used in part a and solve for the width:
Number of DVDs = Length of Shelf / Width of DVD case
Replace the values:
60 = 30 inches / Width of DVD case
To solve for the width of the DVD case, we can multiply both sides of the equation by the width:
60 * Width of DVD case = 30 inches
Width of DVD case = 30 inches / 60
Width of DVD case = 1/2 inch
Therefore, the width of a DVD case should be 1/2 inch or 0.5 inches to fit 60 of them on one shelf.