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A rectangular swimming pool is 20 feet by 28 feet. A deck that has uni

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Bunuel
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A rectangular swimming pool is 20 feet by 28 feet. A deck that has uni [#permalink] New post  10 Jun 2016, 01:19
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67% (02:46) correct 33% (02:57) wrong based on 100 sessions

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A rectangular swimming pool is 20 feet by 28 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 884 square feet. What is the width of the deck?

A. 2 feet
B. 2.5 feet
C. 3 feet
D. 4 feet
E. 5 feet
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OptimusPrepJanielle
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Re: A rectangular swimming pool is 20 feet by 28 feet. A deck that has uni [#permalink] New post  10 Jun 2016, 01:53
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Bunuel wrote:
A rectangular swimming pool is 20 feet by 28 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 884 square feet. What is the width of the deck?

A. 2 feet
B. 2.5 feet
C. 3 feet
D. 4 feet
E. 5 feet


Assume the width of the deck = x
Area of pool and deck = (20 + 2x)*(28 + 2x) =884 {The deck is present at both ends of the length and the breadth, hence we need to add 2x}

(20 + 2x)*(28 + 2x) =884 can be written as
(10 + x)*(14 + x) = 221
140 + 24x + x^2 = 221
x^2 + 24x - 81 = 0
(x + 27)(x - 3) = 0
Hence x = -27 or 3. But a length cannot be negative
Hence width of the deck = x = 3

Correct option: C
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Mo2men
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Re: A rectangular swimming pool is 20 feet by 28 feet. A deck that has uni [#permalink] New post  11 Jun 2016, 07:47
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Let the width =W

Total Area of the pool and deck= (2W+20)(2W+28)

We can Test the answer choices along with unit digit method

A) 2 feet ...........24*32 has unit digit 8..........Eliminate
B) 2.5 feet.........25*33 has unit digit 5..........Eliminate
C) 3 feet............26*34 has unit digit 4...........Hold
D) 4 feet............28*36 has unit digit 8...........Eliminate
E) 5 feet............30*38 has unit digit 0...........Eliminate

Answer: C
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Alex75PAris
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Re: A rectangular swimming pool is 20 feet by 28 feet. A deck that has uni [#permalink] New post  11 Jun 2016, 15:06
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If "a" is the width of the deck

(20 + 2a) * (28 + 2a) = 884, we develop and reduce
a² + 24a = 81, we try the solutions

C fit, 3 + 72 = 81
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Re: A rectangular swimming pool is 20 feet by 28 feet. A deck that has uni [#permalink]
11 Jun 2016, 15:06
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