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When a bucket is two-thirds full of water, the bucket and water weigh

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When a bucket is two-thirds full of water, the bucket and water weigh  [#permalink]

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New post 29 Mar 2019, 00:28
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A
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C
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E

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  65% (hard)

Question Stats:

47% (02:26) correct 53% (02:07) wrong based on 17 sessions

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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

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Re: When a bucket is two-thirds full of water, the bucket and water weigh  [#permalink]

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New post 29 Mar 2019, 03:16
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.
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Re: When a bucket is two-thirds full of water, the bucket and water weigh  [#permalink]

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New post 29 Mar 2019, 03:33
Bunuel wrote:
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



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.
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Re: When a bucket is two-thirds full of water, the bucket and water weigh  [#permalink]

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New post 29 Mar 2019, 03:53
Bunuel wrote:
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


Bucket + (2/3)*Water = a .......... (I)
Bucket + (1/2)*Water = b .........(II)

(I) - (II), we get

(2/3)*Water - (1/2)*Water = a - b
(1/6)*Water = a - b
Water = 6*(a - b)
(1/2)*Water = 3*(a - b)

Adding this to (II),
Bucket + (1/2)*Water + (1/2)*Water = b + 3*(a - b)
Bucket + Water = 3a - 2b

Answer (E)
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Re: When a bucket is two-thirds full of water, the bucket and water weigh  [#permalink]

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New post 29 Mar 2019, 07:17
1
Bunuel wrote:
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


let total weight of water + bucket = 12
so
case 1 : 2/3 full ; 2*12/3 = 8 =a
case 2; 1/2 full; 1/2*12 ; 6=b
substitute a & b in all given options
correct answer will be the one which gives answer as 12
test with e
3*8-2*6 = 12
IMO E
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Re: When a bucket is two-thirds full of water, the bucket and water weigh   [#permalink] 29 Mar 2019, 07:17
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