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A recipe for a mulled cranberry punch calls for 11/4 cups of cranberry

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A recipe for a mulled cranberry punch calls for 11/4 cups of cranberry  [#permalink]

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New post 29 Mar 2018, 23:46
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A recipe for a mulled cranberry punch calls for 11/4 cups of cranberry juice, 3/2 cups of white grape juice, 7/3 cup of water, and 1/4 cup of cinnamon sugar. What is the ratio of the total amount, in cups, of fruit juice to the total amount, in cups, of water and cinnamon sugar in the recipe?

(A) 51 to 31
(B) 31 to 12
(C) 31 to 17
(D) 31 to 51
(E) 12 to 31

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Re: A recipe for a mulled cranberry punch calls for 11/4 cups of cranberry  [#permalink]

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New post 29 Mar 2018, 23:56
Sum of quantity of fruit juices to sum of water and cinnamon sugar in the recipe, implies (11/4+3/2)/(7/3+1/4)= 51:31 Ans A
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A recipe for a mulled cranberry punch calls for 11/4 cups of cranberry  [#permalink]

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New post 30 Mar 2018, 08:43
Bunuel wrote:
A recipe for a mulled cranberry punch calls for 11/4 cups of cranberry juice, 3/2 cups of white grape juice, 7/3 cup of water, and 1/4 cup of cinnamon sugar. What is the ratio of the total amount, in cups, of fruit juice to the total amount, in cups, of water and cinnamon sugar in the recipe?

(A) 51 to 31
(B) 31 to 12
(C) 31 to 17
(D) 31 to 51
(E) 12 to 31

This question gives four ratio parts and asks for the ratio of
(sum of two) Parts : (sum of two) Parts
Given ratio parts:

\(C : G : W : S\)
\(\frac{11}{4}: \frac{3}{2}: \frac{7}{3}: \frac{1}{4}\)

Ratio of fruit juice parts \((C + G)\) to water and sugar parts \((W + S)\)?
Use LCM = \(12\) in order to compare parts to parts on the basis of the same whole.

\(C : G : W : S\)
\(\frac{33}{12}:\frac{18}{12}:\frac{28}{12}:\frac{3}{12}\)

Ratio parts are now based on the same whole.
Use only the numerators.*

Ratio of fruit juice to water and sugar: \(\frac{(C+G)}{(W+S)}=\frac{(33+18)}{(28+3)}=\frac{51}{31}=(51:31)\)

Answer A

*Arithmetically, how "numerators only" works in a part-to-part comparison if parts have the same denominator:
\(\frac{(C+G)}{(W+S)}=\frac{(\frac{33}{12}+\frac{18}{12})}{(\frac{28}{12}+\frac{3}{12})}=\frac{(\frac{51}{12})}{(\frac{31}{12})}=(\frac{51}{12}*\frac{12}{31})=\frac{51}{31}\)

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Re: A recipe for a mulled cranberry punch calls for 11/4 cups of cranberry  [#permalink]

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New post 04 Apr 2018, 17:21
Bunuel wrote:
A recipe for a mulled cranberry punch calls for 11/4 cups of cranberry juice, 3/2 cups of white grape juice, 7/3 cup of water, and 1/4 cup of cinnamon sugar. What is the ratio of the total amount, in cups, of fruit juice to the total amount, in cups, of water and cinnamon sugar in the recipe?

(A) 51 to 31
(B) 31 to 12
(C) 31 to 17
(D) 31 to 51
(E) 12 to 31


We can create the ratio:

(11/4 + 3/2)/(7/3 + 1/4)

Multiplying by 12/12, we have:

(33 + 18)/(28 + 3) = 51/31

Answer: A
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Re: A recipe for a mulled cranberry punch calls for 11/4 cups of cranberry   [#permalink] 04 Apr 2018, 17:21
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