Question

To meet building codes, a building must have a roof no taller than 74 feet. An architect is designing a museum with a 14 ½ foot ground floor, and 12 foot 3 inch upper floors (including supports) How many floors, including the ground floor, can the building have?

Answer 1

Total allowed height is 74 ft. This equals 14 1/2 feet plus (12 ft 3 in)x, where x is the number of floors above the ground floor:

74 ft = 14.50 ft + (12.25 ft / floor)x. Solve for x:

First, subtract 14.50 ft from both sides of this eq'n:

(74 - 14.50) feet + 12.25x

Then 59.50 feet = (12.25 feet / floor) x

Solving for x: 59.50 feet
-------------------- = 4.9 floors.
12.25 feet
-------------
floor

This must be rounded down. The total height of the new building will then be:

14.5 feet + (12.25 feet
------------- ) (4), or 59.50 feet + 49 feet = 63.5 feet
floor

because there's not enough room vertically for a 5th floor above the ground floor.

Answer: 4 floors may be built above the ground floor.

Answer 2

Building can have 4 floors.

Explanation:

Height of the ground floor is 14.5 foot and height of upper floors = 12 foot 3 inches or 12.25 foot per floor

Let there are x floors in the building.

Total height of the building = 74 foot

Therefore, total height of the building = Height of the ground floor + Height of the upper floors

74 = 14.5 + 12.25x

74 - 14.5 = 12.25x

12.25x = 59.5

x =
`(59.5)/(12.25)`

x = 4.9 floors

Therefore, the building can have 4 floors.