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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?

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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:

Building can have 4 floors.

Step-by-step 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 = [tex]\frac{59.5}{12.25}[/tex]

x = 4.9 floors

Therefore, the building can have 4 floors.

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