John is making a bookcase that is
72 3/8inches tall, he wants 5 equally spaced shelves. Eacg self is 3/8 inche thick. tell him where to drill the holes.
If the first shelf is at the bottom,there will be 5 equally spaced slots, starting from the bottom. The slots (center to center will be then the height less one shelf thickness..think about that top board) slot thickness, center to center will be.
72 3/8 - 3/8= 72
then divide by five..14 2/5 inches.
So, bottom and top holes at 3/16 from then ends.
Then first the subsequent holes each 14 2/5 inches.
Check: top+ 5 book slots(center to center)=?
3/8+ 5*14 2/5 = you do it.
check my thinking. A drawing might help.
To determine the spacing for the shelves on John's bookcase, we need to subtract the thickness of the shelves from the total height of the bookcase and divide it by the number of shelves plus one.
First, let's calculate the height of each shelf:
Total height of bookcase = 72 3/8 inches
Thickness of each shelf = 3/8 inches
Height of each shelf = (Total height of bookcase - Thickness of each shelf) / (Number of shelves + 1)
Height of each shelf = (72 3/8 inches - 3/8 inches) / (5 shelves + 1)
= (72 3/8 inches - 3/8 inches) / 6
Now, let's calculate this height:
To subtract fractions, we need to convert both fractions to have a common denominator, which is 8 in this case.
72 3/8 inches can be written as (72 * 8 + 3)/8 = 579/8 inches.
3/8 inches is already in the correct format.
Therefore, our equation becomes:
Height of each shelf = (579/8 inches - 3/8 inches) / 6
= (576/8 inches) / 6
= 72 inches / 6
= 12 inches
So, each shelf on John's bookcase should be positioned 12 inches apart from each other. Therefore, he should drill the holes for the shelves at 12-inch intervals starting from the bottom.