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16 Apr 2021, 05:15
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D
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Difficulty:
25%
(medium)
Question Stats:
78% (01:24) correct
22%
(01:59)
wrong
based on 126
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A rectangular floor having perimeter of 16 meters is to be covered with square carpets that measure 1 meter by 1 meter each and cost $6 apiece. What is the maximum possible cost for the number of square carpets needed to cover the rectangular floor if the sides of the floor are integers?
(A) $42
(B) $72
(C) $90
(D) $96
(E) $120
(A) $42
(B) $72
(C) $90
(D) $96
(E) $120
23 Apr 2021, 07:23
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P=2a + 2b
2a + 2b = 16
a + b = 8
Now, in order to find the maximum cost we need to ‘maximize’ the area of a rectangular.
We can do so simply by trying to put different values of (a) and (b) in the equation above and then finding the area of a rectangular:
a + b = 8
1) 1 + 7 -> S= a*b = 1*7= 7
2) 2 + 6 -> S= 2*6 = 12
3) 3 + 5 -> S= 3*5 = 15
4) 4 + 4 -> S= 4*4 = 16
S = 16 is the maximum possible value of the area. It means that 16 square carpets are needed to cover the floor.
1 carpet is 6$ -> 16 carpets: 16*6 = 96.
Answer is D.
Posted from my mobile device
2a + 2b = 16
a + b = 8
Now, in order to find the maximum cost we need to ‘maximize’ the area of a rectangular.
We can do so simply by trying to put different values of (a) and (b) in the equation above and then finding the area of a rectangular:
a + b = 8
1) 1 + 7 -> S= a*b = 1*7= 7
2) 2 + 6 -> S= 2*6 = 12
3) 3 + 5 -> S= 3*5 = 15
4) 4 + 4 -> S= 4*4 = 16
S = 16 is the maximum possible value of the area. It means that 16 square carpets are needed to cover the floor.
1 carpet is 6$ -> 16 carpets: 16*6 = 96.
Answer is D.
Posted from my mobile device
18 Aug 2021, 07:34
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the questions says "rectangular floor", so the maximum possible should be 15*6= 90$. Width and length cannot be the same. Otherwise, it would become a square, which is conflict with the given information. Answer C
