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Wall-to-wall carpeting is installed in a certain hallway. Th

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sandy
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Wall-to-wall carpeting is installed in a certain hallway. Th [#permalink] New post   14 Jun 2018, 14:18
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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
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D
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Re: Wall-to-wall carpeting is installed in a certain hallway. Th [#permalink] New post   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


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
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sandy
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Re: Wall-to-wall carpeting is installed in a certain hallway. Th [#permalink] New post   05 Jul 2018, 02:56
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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!
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Re: Wall-to-wall carpeting is installed in a certain hallway. Th [#permalink]
05 Jul 2018, 02:56
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