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A set of eight built-in bookshelves is to be constructed in a room. The floor-to-ceiling clearance is 7 ft 5 in. Each shelf is 1 in. thick. An equal space is to be left between the shelves, the top shelf and the ceiling, and the bottom shelf and the floor. How many inches should there be between each shelf and the next? (There is no shelf against the ceiling and no shelf on the floor.

Answer :

Answer: 12

Step-by-step explanation:

Space between each shelf and the next is equals to 9inches while constructing set of eight shelves.

What is space?

" Space is defined as the area left between two given object."

Conversion used

1ft = 12inches

According to the question,

Set of bookshelves to be constructed = 8

Floor to ceiling clearance = 7ft 5in.

                                           = (7 × 12 + 5)inches

                                           = 89 inches

Thickness of each shelf = 1inch

'x' represents the equal space left between the shelves  top and the ceiling.

Therefore,

Total space left  between the 8 shelves  top and the ceiling = 9x

From the given data and condition we have,

Total space left + (set of shelves × thickness) = Floor to ceiling clearance

⇒9x + 8× 1 = 89

⇒[tex]9x + 8 = 89[/tex]

⇒[tex]9x = 89 -8[/tex]

⇒[tex]9x = 81[/tex]

⇒ [tex]x=\frac{81}{9}[/tex]

⇒[tex]x=9[/tex] inches

Hence, space between each shelf and the next is equals to 9inches while constructing set of eight shelves.

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