Answer
$x=10$ $inches$
Work Step by Step
Step 1:
Since we know the thickness of the shelves, we can add them to find the space taken by the shelves themselves.
We assign the variables:
$a=$ thickness of each shelf
$b =$ total thickness occupied by the shelves
The total thickness occupied by the shelves is then
$b=8a$ $\rightarrow$ because it is a set of eight.
$b=8(1 in)=8$ $inches$
Step 2:
Find the space remaining in the clearance.
We assign the variables:
$c=$ floor to ceiling clearance $= 8ft$ $2 in$
$d=$ floor to ceiling clearance minus total thickness occupied by the shelves.
So,
$d=$ $ 8ft$ $2 in$ $-8in$ $\rightarrow$ remember 1 ft = 12 inches.
$d=98in - 8in=90in$
Step 3:
For this step, refer to the diagram in the answer.
Since no shelf is against the floor or the ceiling, then we have $9$ empty spaces between the shelves.
Let x = space between each shelf and the next.
So,
$x=\frac{d}{9}=\frac{90in}{9}=10in$
