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29 Mar 2019, 00:28
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Difficulty:
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Question Stats:
67% (02:40) correct
33%
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When a bucket is two-thirds full of water, the bucket and water weigh \(a\) kilograms. When the bucket is one-half full of water the total weight is \(b\) kilograms. In terms of \(a\) and \(b\), what is the total weight in kilograms when the bucket is full of water?
(A) 2a/3 + b/3
(B) 3a/2 - b/2
(C) 3a/2 + b
(D) 3a/2 + 2b
(E) 3a - 2b
(A) 2a/3 + b/3
(B) 3a/2 - b/2
(C) 3a/2 + b
(D) 3a/2 + 2b
(E) 3a - 2b
29 Mar 2019, 03:16
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So we know that 2/3 full equals to a kg, so when the bucket is completely full it will weigh (in terms of a) = 3a/2 kg
Similarly, since we know that 1/2 full equals to b kg, when the bucket is completely full it will weigh (in terms of b now) = 2b kg
So 3a/2 = 2b <=> 3a = 4b
By substituting in E, we see that it is indeed 3a-2b since 3a-2b=4b-2b=2b, which is the total weight in terms of b.
P.S. Since we have calculated that the TOTAL weight in terms of a is "3a/2", all answer choices that have this term plus or minus something, will be incorrect. This leaves us only A and E. E is the correct.
Similarly, since we know that 1/2 full equals to b kg, when the bucket is completely full it will weigh (in terms of b now) = 2b kg
So 3a/2 = 2b <=> 3a = 4b
By substituting in E, we see that it is indeed 3a-2b since 3a-2b=4b-2b=2b, which is the total weight in terms of b.
P.S. Since we have calculated that the TOTAL weight in terms of a is "3a/2", all answer choices that have this term plus or minus something, will be incorrect. This leaves us only A and E. E is the correct.
rkbrohit90
29 Mar 2019, 03:33
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Bunuel
let weight of full water be "w" and weight of bucket be "y".
SO equation 1 states= 2/3(w) +y= a
euation 2 states = 1/2(w) +y=b
(1)-(2)
(2/3-1/2)w=a-b
w(4-3)/6=a-b
w=6(a-b)
using this in equation (2) we get
1/2w +y=b
1/2*(6(a-b))+ y=b
y= b-3(a-b)
total weight of ful bucket = w+y = 6(a-b) +b-3(a-b) =3a-2b.
