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Isn't the area of uncovered floor 28 percemt of 200?

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Bunuel
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?


A. 28
B. 56
C. 80
D. 200
E. 560

Hi ..
72% of total =9*16
Don't multiply, may save time while dividing..

So \(\frac{72}{100}*total=9*16.......total =9*16*\frac{100}{72}\)
Divide both by 9 first..
\(total = 16*\frac{100}{8}\)
Now divide by 8
\(total=2*100=200\)

D

Shouldn't the ans be 0.28 x 200?as it asks for uncovered area

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Bunuel
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?


A. 28
B. 56
C. 80
D. 200
E. 560

Hi ..
72% of total =9*16
Don't multiply, may save time while dividing..

So \(\frac{72}{100}*total=9*16.......total =9*16*\frac{100}{72}\)
Divide both by 9 first..
\(total = 16*\frac{100}{8}\)
Now divide by 8
\(total=2*100=200\)

D
Hi chetan2u
Here is my approach.
% of floor___Area
72 ----------> 9*16
28 ----------> \(\frac{(9*16)*28}{72}\)
--> Area of uncovered floor = \(\frac{(9*16)*28}{72}=\frac{(9*16)*28}{9*8}=2*28=56\) -> Answer B.
According to your solution, shouldn't 200 be the area of total floor, not the area of uncovered floor ?
Please correct me if I am wrong.
Thank you.
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chetan2u
Bunuel
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?


A. 28
B. 56
C. 80
D. 200
E. 560

Hi ..
72% of total =9*16
Don't multiply, may save time while dividing..

So \(\frac{72}{100}*total=9*16.......total =9*16*\frac{100}{72}\)
Divide both by 9 first..
\(total = 16*\frac{100}{8}\)
Now divide by 8
\(total=2*100=200\)

D
Hi chetan2u
Here is my approach.
% of floor___Area
72 ----------> 9*16
28 ----------> \(\frac{(9*16)*28}{72}\)
--> Area of uncovered floor = \(\frac{(9*16)*28}{72}=\frac{(9*16)*28}{9*8}=2*28=56\) -> Answer B.
According to your solution, shouldn't 200 be the area of total floor, not the area of uncovered floor ?
Please correct me if I am wrong.
Thank you.


You are absolutely correct ..
I have answered for the total area, but it has to be for uncovered..
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Bunuel
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?


A. 28
B. 56
C. 80
D. 200
E. 560

Here 72% = 16*9 = 144
Therefore, uncovered floor = 28%
Now, since 72% = 144
Therefore, 28% = (144/72)*28 = 56

Hence B is the answer.
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Bunuel
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?


A. 28
B. 56
C. 80
D. 200
E. 560

Note: we are looking for the are of the Uncovered Floor. Covered is 72% . So uncovered area is 28%.

covered floor = 16*9 = 144.

72% represents 144

1% represents 144/72

28% represents 144*28 / 72


= 56.

The best answer is B.
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Bunuel
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?


A. 28
B. 56
C. 80
D. 200
E. 560

\(\frac{16*9}{72}*28\)

= 56, Answer must be (B)

PS : Skippe steps in between , anyone requirng explainations please feel free to revert. :grin: :grin: :grin:
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Bunuel
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?


A. 28
B. 56
C. 80
D. 200
E. 560

Letting n = the area of the floor, we can create the following equation:

(9 x 16) = 0.72n

144 = 0.72n

200 = n

So the area of the uncovered floor is 200 - 144 = 56 square feet.

Answer: B
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We can use proportionality rules to solve this question. If we consider the total area of rectangular area = 100

Total rectangular area Area covered Area not covered
Assumption 100 72 28
x 2
Given 200 9*16= 144 56

We notice that the ratio between the percentage of area covered and the area covered is 2 ( 144/ 72).

Area not covered = 28* 2 = 56.(B)
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