Question

A furniture company makes a variety of wooden bookcases. The height of each shelf space is 13 inches. The top and bottom are each 2 inches thick and the pieces separating the shelf spaces are each ¾ -inch thick. Write an equation that models the total height h of a bookcase that contains n shelf spaces.

Answer 1

The total height of a bookcase with n shelf spaces can be found using the equation h = 13n + 0.75(n - 1) + 4, where h is the total height, and n is the number of shelf spaces.

Step-by-step explanation:

The equation that models the total height h of a bookcase with n shelf spaces is given by adding together the heights of all separate components of the bookcase:

• The combined height of all shelf spaces (13 inches each)
• The combined thickness of the top and bottom of the bookcase (2 inches each)
• The combined thickness of the pieces that separate the shelf spaces (3/4 inch each)

To calculate the total height:

1. Multiply the number of shelf spaces, n, by the height of each shelf space, 13 inches.
2. Multiply the number of shelves minus one, n - 1, by the thickness of the separators, 3/4 inch, since there is a separator above each shelf except the top one.
3. Add the thickness of the top and bottom of the bookcase, 4 inches total (2 inches each).
4. Add the results from steps 1, 2, and 3 to get the total height h.

The equation can be written as:

h = 13n + 0.75(n - 1) + 4