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.

For the first question the answer is a, for the second c, for the third d, for the 4th b, for the 5th a