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Square feet less a fraction

The area of a room is 99-3/7 square feet.  The area of the kitchen is 1-3/4 the area of room.  If the length of kitchen is 14-1/2 feet how wide is the kitchen?  I have no idea where to even start, help!!
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3 Answers

I came to the same conclusion as Terri:  To wit, the area of the kitchen is more than the area of the room.  I am uncertain whether this is because of the way the question was written:  Is it possible that the question was transcribed unclearly?
I think this would be easier to use improper fractions since you are going to have to multiply.  Also, since 2-11/63 is NOT a reasonable width, possibly the area of the kitchen is 1.75 the area of the room (not 1 minus 3/4 = 1/4).  So here goes:
 
The area of the room is 99-3/7 = 696/7.  The area of the kitchen is 1-3/4=7/4 of the area of the room (WHICH IS MORE).  Therefore, the area of the kitchen is 696/7*7/4 = 696/4 (since the 7/7 reduces to 1) which equal 174 square feet for the kitchen area.
 
If the length of the kitchen is 14-1/2 = 29/2 feet, then solving Area = Length * Width...
174 = 29/2 * W ==> multiply both sides by 2 and divide both sides by 29 to clear the multiplier of the    variable [you could have chosen to set this up as a proportion to solve the equation 174/1 = 29W/2]
2/29(174/1) = 2/29 (29/2 * W)
348/29 = W ==> multiply across the numerators and across the denominators
12 = W  ==> division
 
Therefore the Width of the Kitchen is 12 feet. 
 
NOTE - the Area of the Kitchen is 14.5 ft X 12 ft = 174 ft2 which is clearly MORE than the area of the room (since it is 1.75 times it) 
area = length x width
(1/4)(99-3/7) = (14-1/2)W, since the area of the kitchen is 1-3/4 = 1/4 of the area of the room
Solve for W,
W = 2-11/63 ft^2 <==Answer