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Re M0728
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15 Sep 2014, 23:35
Official Solution:To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. From an average lemon one can squeeze out 0.4 cups of 5% citric acid. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. If she has sugar and water in abundance, how much water will Marta use? A. 2 pt. B. 6 pt. C. 12 pt. D. 15 pt. E. 100 pt. Standard recipe requires: 4 lemons and 2 pints of water. 4 lemons contain \(4*0.4*\frac{5}{100}=\frac{8}{100}\) cups of citric acid; Now, Marta has \(4*\frac{12}{100}=\frac{48}{100}\) cups of citric acid, so 6 times as many as the standard recipe requires (\(\frac{48}{8}=6\)), which means that she'll need 6 times as much water as the standard recipe requires. Hence she'll need \(6*2=12\) pints of water. Answer: C
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Re: M0728
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15 Jun 2015, 11:09
Bunuel wrote: Official Solution:
To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. From an average lemon one can squeeze out 0.4 cups of 5% citric acid. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. If she has sugar and water in abundance, how much water will Marta use?
A. 2 pt. B. 6 pt. C. 12 pt. D. 15 pt. E. 100 pt.
Standard recipe requires: 4 lemons and 2 pints of water. 4 lemons contain \(4*0.4*\frac{5}{100}=\frac{8}{100}\) cups of citric acid; Now, Marta has \(4*\frac{12}{100}=\frac{48}{100}\) cups of citric acid, so 6 times as many as the standard recipe requires (\(\frac{48}{8}=6\)), which means that she'll need 6 times as much water as the standard recipe requires. Hence she'll need \(6*2=12\) pints of water.
Answer: C Can we start a discussion here and revive this task here a bit with the following questions? Since this is a mixture problem, how do we account for the different percentages of citric acid? I do not see this in the answer, it's not clear for me. The recipe requires 4 lemons i.e. 4*0.4 cups * 5%? Does this mean, the recipe requires 8 of what... (what? what's the measure after doing the calculations )
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Joined: 09 Feb 2015
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Re: M0728
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25 Jun 2015, 00:25
yes please expain why did u convert the % concentration in to number of cups



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Re: M0728
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12 Jul 2015, 21:52
My solution: Given: Lemon one: 0.4*5/100 = 1/50 (citric acid) 4 cups of 12% citric acid = 4*12/100 = 12/25 = 24/50 (citric acid) => We have 24 lemons from 4 cups of 12% citric acid. 24/4 = 6 cups. => Pints of water: 6*2 = 12. Is it right?



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Re: M0728
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06 Sep 2016, 12:01
Bunuel wrote: To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. From an average lemon one can squeeze out 0.4 cups of 5% citric acid. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. If she has sugar and water in abundance, how much water will Marta use?
A. 2 pt. B. 6 pt. C. 12 pt. D. 15 pt. E. 100 pt. Bunuel, Need to your help in understanding where I am doing the mistake: i am converting everything in to 5% concentrate lets find how much of water will be required to convert the 12% to 5% concentration 12  0 (pure water) v 5 . ^ 57 5/7= 4/x x= 5.6 pints of water is required to dilute the 12% 4 cups to 5% concentration. now, 1 lemon can have 0.4 cups of 5% of citric acid, so 4 *0.4 =1.6 cup so 1. 6 cup require 2 pints of water for actual recipe. So we have 4 cups(already diluted 12% to 5%) will require 5 pints of water so total water required is 5.6 +5 ==>10.6 (not listed though!)



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Joined: 15 Oct 2016
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In this case , we dont have to use the standard Part/whole = % formula that is commonly used in mixtures problems.
Here the question first provides standard lemonade recipe  4 lemons, 30 ounces of sugar and 2 pints of water.  (A) Since question asks for water requirement, we can ignore the sugar content. So, standard recipe says for 4 lemons , we need 2 pints of water. We also understand that One Lemon = 0.4 cups of 5% citric acid. (B)
Correlating (A) and (B), we understand that in a standard lemonade recipe , we will use 1.6 cups of 5% citric acid with 2 pints of water.
From now on, the question is purely relations...
If 1.6 Cups of 5% citric acid > 2 pints , then 1.6 cups of 12% citric acid > X Using inversion, 5x = 12*2 , solving for x , we get x = 4.8 pints. So, if we had the same 1.6 cups of higher concentration citric acid ( 12%), then we need more water i.e 4.8 pints.
Now, the final step ,
If 1.6 cups of 12% citric acid requires 4.8 pints of water, then how much will 4 cups of 12% citric acid require .
Applying same relation , 1.6 x = 4.8 * 4, solving for x we will get 12 pints , the answer



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Re M0728
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30 Dec 2017, 12:35
I think this is a highquality question and I agree with explanation. Take into consideration the quantity, concentration, and water. The proportion of concetration must be keep the same. Therefore we have the equation:
L*0.4*(5%)/2pt = 4*(12%)/X
X=12



Intern
Joined: 30 Jan 2018
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Why would we assume that all 4 cups of the 12% acid needs to be used. We only need to dilute 1 cup to get a 5% mixture (12%>5%). Why would Martha not use 1 cup of the 12% mixture to get the 5% diluted acid? Clearly the answer has choices which require all 4 but that would take some time to figure out. This is a high quality question. I wish the question had specified that we need to use all 4 cups of the acid for dilution.










