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

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
When a bucket is two-thirds full of water, the bucket and water weigh  [#permalink]

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29 Mar 2019, 00:28
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Difficulty:

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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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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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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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)

Bucket + (1/2)*Water + (1/2)*Water = b + 3*(a - b)
Bucket + Water = 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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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
test with e
3*8-2*6 = 12
IMO E
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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