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?

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.

 4 floors may be built above the ground floor.

Hope i can you!

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