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# Three different types of wine are 10%, 12%, and 14% alcohol, respectiv

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Math Expert
Joined: 02 Sep 2009
Posts: 58379
Three different types of wine are 10%, 12%, and 14% alcohol, respectiv  [#permalink]

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01 May 2017, 02:35
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Difficulty:

15% (low)

Question Stats:

80% (02:06) correct 20% (02:24) wrong based on 144 sessions

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Three different types of wine are 10%, 12%, and 14% alcohol, respectively. If a liters of the 10% wine, b liters of the 12% wine, and c liters of the 14% wine are combined to form a+b+c liters of an 11% alcohol blend, then what is a in terms of b and c?

A. b + 3c

B. c + 3b

C. 2b + 3c

D. (c + b)/4

E. b + c

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Re: Three different types of wine are 10%, 12%, and 14% alcohol, respectiv  [#permalink]

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01 May 2017, 03:48
1
Bunuel wrote:
Three different types of wine are 10%, 12%, and 14% alcohol, respectively. If a liters of the 10% wine, b liters of the 12% wine, and c liters of the 14% wine are combined to form a+b+c liters of an 11% alcohol blend, then what is a in terms of b and c?

A. b + 3c

B. c + 3b

C. 2b + 3c

D. (c + b)/4

E. b + c

10% of a + 12% of b + 14% of c = 11% of (a+b+c)

i.e. 10a + 12b + 14 c = 11a + 11b + 11c
i.e. a = b+3c

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Re: Three different types of wine are 10%, 12%, and 14% alcohol, respectiv  [#permalink]

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01 May 2017, 05:02
1
We can use allegations to solve the problem

a(10) b(12)
total(11)
1 : 1

a(10) c(14)
total(11)
1 : 3

Hence a in the form of b & c will be b+3c(Option A)
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Re: Three different types of wine are 10%, 12%, and 14% alcohol, respectiv  [#permalink]

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01 May 2017, 23:37
its a straight approach,,
i will prefer alligation approach when there are two items

back to the question,,

.1 a + .12 b + .14c = .11(a+b+c)

solving we get a = b + 3c
ans A
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Re: Three different types of wine are 10%, 12%, and 14% alcohol, respectiv  [#permalink]

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02 May 2017, 23:34
New Solution = Sol A + Sol B + Sol C ---> (A + B + C) ---------------------------- eq 1

Since, New Solution = (A + B + C) ---> New Solution is 14% alcohol ----> .14 (A+B+C) ------ eq 2
Sol A => A = .10a ------ eq 3
Sol B => B = .12b ------ eq 4
Sol C => C = .14c ------ eq 5

Equate values of eq 2,3,4 and 5 in eq 1

=> .10a + .12b + .14c = .11 (a+b+c)
=> 10a + 12b + 14c = 11 (a+b+c)
=> 12b-11b + 14c - 11c = 11a -10a
=> b + 3c = a

IMO Ans: A
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Re: Three different types of wine are 10%, 12%, and 14% alcohol, respectiv  [#permalink]

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06 May 2017, 17:12
Bunuel wrote:
Three different types of wine are 10%, 12%, and 14% alcohol, respectively. If a liters of the 10% wine, b liters of the 12% wine, and c liters of the 14% wine are combined to form a+b+c liters of an 11% alcohol blend, then what is a in terms of b and c?

A. b + 3c

B. c + 3b

C. 2b + 3c

D. (c + b)/4

E. b + c

We can create the following equation and isolate a:

0.1a + 0.12b + 0.14c = 0.11(a + b + c)

10a + 12b + 14c = 11(a + b + c)

10a + 12b + 14c = 11a + 11b + 11c

b + 3c = a

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Re: Three different types of wine are 10%, 12%, and 14% alcohol, respectiv  [#permalink]

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13 Oct 2018, 08:50
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Re: Three different types of wine are 10%, 12%, and 14% alcohol, respectiv   [#permalink] 13 Oct 2018, 08:50
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