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A contractor uses half of the available concrete to pour an 8-foot by 12-foot rectangular base for a monument. If she uses the rest of the concrete to create a uniform-width walkway all the way around the base of the monument, using the same amount of concrete per square foot as for the base, what is the maximum possible width of the walkway?
A. 1 foot
B. 2 feet
C. 3 feet
D. 4 feet
E. 6 feet
Are You Up For the Challenge: 700 Level Questions
A. 1 foot
B. 2 feet
C. 3 feet
D. 4 feet
E. 6 feet
Are You Up For the Challenge: 700 Level Questions
27 Feb 2022, 15:22
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Bunuel
A contractor uses half of the available concrete to pour an 8-foot by 12-foot rectangular base for a monument. If she uses the rest of the concrete to create a uniform-width walkway all the way around the base of the monument, using the same amount of concrete per square foot as for the base, what is the maximum possible width of the walkway?
A. 1 foot
B. 2 feet
C. 3 feet
D. 4 feet
E. 6 feet
A. 1 foot
B. 2 feet
C. 3 feet
D. 4 feet
E. 6 feet
Breaking Down the Info:
The current rectangular base is 96 square ft, which means we have that much left for the walkway as well. The maximum width gives us a total area of 96*2, so by setting the width as x feet we have \((12 + 2x)(8 + 2x) = 96*2\).
\((6 + x)(4 + x) = 48\), hence we need to break 48 into y = x + 4 and y + 2. 48 = 6*8 accomplishes that, so \(4 + x = 6\) and \(x = 2\).
Answer: B
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