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In the standard formulation of a flavored drink the ratio by volume of

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In the standard formulation of a flavored drink the ratio by volume of [#permalink]

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New post 12 Oct 2010, 10:38
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In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the "sport" formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the "sport" formulation contains 3 ounces of corn syrup, how many ounces of water does it contain?

A. 15
B. 30
C. 45
D. 60
E. 90
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Aug 2017, 02:44, edited 2 times in total.
Renamed the topic and edited the question.

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Re: In the standard formulation of a flavored drink the ratio by volume of [#permalink]

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New post 12 Oct 2010, 10:50
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mrinal2100 wrote:
In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30.
In the "sport" formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation,
and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the "sport"
formulation contains 3 ounces of corn syrup, how many ounces of water does it contain?

A)15
B)30
C)45
D)60
E)90

[Reveal] Spoiler:
b


Standard: \(\frac{f}{\frac{c}{w}}=\frac{1}{\frac{12}{30}}\);

Sport: "the ratio of flavoring to corn syrup is three times as great as in the standard" --> \(\frac{F}{C}=3\frac{f}{c}=3*\frac{1}{12}=\frac{1}{4}\) and "the ratio of flavoring to water is half that of the standard formulation" --> \(\frac{F}{W}=\frac{1}{2}*\frac{f}{w}=\frac{1}{2}*\frac{1}{30}=\frac{1}{60}\).

So sport: \(\frac{F}{\frac{C}{W}}=\frac{1}{\frac{4}{60}}\). Now, if \(C=4*\frac{3}{4}=3\) ounces then \(W=60*\frac{3}{4}=45\) ounces.

Or: as \(\frac{F}{\frac{C}{W}}=\frac{1}{\frac{4}{60}}\) then \(\frac{C}{W}=\frac{4}{60}=\frac{1}{15}=\frac{3}{45}\), so if \(C=3\) then \(W=45\).

Answer: C.
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Re: In the standard formulation of a flavored drink the ratio by volume of [#permalink]

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New post 12 Oct 2010, 12:28
I also got C
F:C:W
1:12:30

F:C is 3x
3:12

F:W is 1/2
1:60

so...
F=3 (1 * 3)
C=12 (nothing changed)
W=180 (30*=60 for halfing the ratio and then 3*60 to bring it back into the correct ratio with F)

Ratio:
F:C:W
3:12:180

12/4=3oz of C
so...
180/4=45oz of water

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Re: In the standard formulation of a flavored drink the ratio by volume of [#permalink]

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New post 12 Oct 2010, 12:35
so if i've got it right, 1 : 12 : 30 is equal to f/c/w where the ratio of flavoring to water can be literarily written as 1/30 right ?

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Re: In the standard formulation of a flavored drink the ratio by volume of [#permalink]

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New post 12 Oct 2010, 12:37
in this case case 3/4 is the unknown multiplier right ?

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Re: In the standard formulation of a flavored drink the ratio by volume of [#permalink]

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New post 12 Oct 2010, 12:37
whichscore wrote:
so if i've got it right, 1 : 12 : 30 is equal to f/c/w where the ratio of flavoring to water can be literarily written as 1/30 right ?


Yup.
Flavor or Corn Syrup is 1:12
Flavor to Water is 1:30

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Re: In the standard formulation of a flavored drink the ratio by volume of [#permalink]

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New post 12 Aug 2017, 01:41
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Hi,
is the OA wrong in this question? Shouldn't it be "c" as in Bunuel's solution?

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Re: In the standard formulation of a flavored drink the ratio by volume of [#permalink]

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New post 12 Aug 2017, 02:45

Kudos [?]: 128621 [0], given: 12180

Re: In the standard formulation of a flavored drink the ratio by volume of   [#permalink] 12 Aug 2017, 02:45
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