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

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

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.­