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.

2 1/2 feet = 30 inches

30 / (9/16)

30 * (16/9) = 480 / 9 = 53.3 = 53 DVDs on one shelf

b. 30/60 = ?

I do not understand how to do part B.

because the original shelf is 2 1/2 feet and that will hold 53 DVDs but how to you figure out how much shelf (in feet) is needed for 60 DVDs?
Am I dividing 30/60 which is 2 and adding it to 2 1/2?

To find the number of DVDs that will fit on one shelf, we need to determine how many DVDs can fit in the 2 1/2 feet length of the shelf.

To do this, we will convert the length of the shelf to inches. Since there are 12 inches in a foot, 2 1/2 feet is equal to (2 * 12) + (1/2 * 12) = 24 + 6 = 30 inches.

Next, we need to find how many DVD cases can fit within the 30 inches of the shelf length. To do this, we divide the shelf length by the width of the DVD case.

a. DVD cases are 9/16 inch wide. To find how many DVD cases can fit on one shelf, we divide the shelf length (30 inches) by the width of the DVD case (9/16 inch).

First, we convert the width of the DVD case to inches:
9/16 inch = (9/16) * 1 inch = 0.5625 inches

Now we divide the shelf length by the width of the DVD case:
30 inches / 0.5625 inches ≈ 53.33

Therefore, Juan can fit approximately 53 DVDs on one shelf.

b. To find out how wide a DVD case would have to be in order for 60 of them to fit on one shelf, we can rearrange the formula above.

Let "x" be the width of the DVD case. We know that 30 inches is the length of the shelf. We can set up the equation as below:

30 inches / x inches = 60 DVD cases

To find the width of the DVD case in feet, we need to convert the answer to feet.

First, we convert the width of the DVD case from inches to feet:
x feet = x inches / 12

To find the width of the DVD case in feet, we can rearrange the equation as follows:

30 inches / (x inches / 12) = 60 DVD cases

Now we can simplify the equation to solve for x:

30 * 12 / 60 = x

x = 6 inches

Therefore, a DVD case would have to be 6 inches wide (or 0.5 feet) in order for 60 of them to fit on one shelf.

Good job, just change the fractions into improper fractions, and divide (but switch the reciprocal) :) :0 :D

How do we do number 4