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Wall-to-wall carpeting is installed in a certain hallway. Th
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14 Jun 2018, 14:18
14 Jun 2018, 14:18
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Question Stats:
72% (02:05) correct
27% (02:17) wrong based on 36 sessions
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Wall-to-wall carpeting is installed in a certain hallway. The carpeting costs $4.25 per square foot. If the perimeter of the hallway (in feet) is equal to 44% of the area of the hallway (in square feet) and the hallway is 50 feet long, how much did the carpeting cost?
(A) $182.50
(B) $212.50
(C) $505.25
(D) $1,062.50
(E) $1,100.00
(A) $182.50
(B) $212.50
(C) $505.25
(D) $1,062.50
(E) $1,100.00
Re: Wall-to-wall carpeting is installed in a certain hallway. Th
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03 Jul 2018, 05:01
03 Jul 2018, 05:01
sandy wrote:
Wall-to-wall carpeting is installed in a certain hallway. The carpeting costs $4.25 per square foot. If the perimeter of the hallway (in feet) is equal to 44% of the area of the hallway (in square feet) and the hallway is 50 feet long, how much did the carpeting cost?
(A) $182.50
(B) $212.50
(C) $505.25
(D) $1,062.50
(E) $1,100.00
(A) $182.50
(B) $212.50
(C) $505.25
(D) $1,062.50
(E) $1,100.00
Here ,
Length = 50
Breadth = B
from the statement we can write as:
2 * (Length + Breadth) = 0.44 (Length * Breadth)
or 2 * (50 + B) = 0.44 * 50B
or 50 + B = 11B
or B = 5
Now area of the hallway = \(50 * 5 =250 feet^2\)
Therefore cost = 250 * 4.25 = $1062.5
Re: Wall-to-wall carpeting is installed in a certain hallway. Th
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05 Jul 2018, 02:56
05 Jul 2018, 02:56
Expert Reply
Explanation
The equation for the perimeter of a space is 2W + 2L = P, where W is width and L is length.
The equation for the area is A = W × L. Thus,
\(0.44(W \times L) = 2W + 2L\)
\(0.44(50W) = 2W + 2(50)\)
\(22W = 2W + 100\)
\(20W = 100\)
\(W = 5\)
If W = 5 and L = 50, then the area of the hallway is 250 sq. ft., and the total cost is: $4.25 × 250 = $1,062.50.
Hence option D is correct!
The equation for the perimeter of a space is 2W + 2L = P, where W is width and L is length.
The equation for the area is A = W × L. Thus,
\(0.44(W \times L) = 2W + 2L\)
\(0.44(50W) = 2W + 2(50)\)
\(22W = 2W + 100\)
\(20W = 100\)
\(W = 5\)
If W = 5 and L = 50, then the area of the hallway is 250 sq. ft., and the total cost is: $4.25 × 250 = $1,062.50.
Hence option D is correct!
