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M07-28

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M07-28 [#permalink]

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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.
[Reveal] Spoiler: OA

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Re M07-28 [#permalink]

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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: M07-28 [#permalink]

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New post 15 Jun 2015, 12:09
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 :oops: :cry: )
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Re: M07-28 [#permalink]

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New post 25 Jun 2015, 01:25
yes please expain why did u convert the % concentration in to number of cups
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Re: M07-28 [#permalink]

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New post 12 Jul 2015, 22:52
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: M07-28 [#permalink]

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New post 06 Sep 2016, 13:01
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 .
^
5--------7


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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M07-28 [#permalink]

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New post 13 Jun 2017, 02:54
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 M07-28 [#permalink]

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New post 30 Dec 2017, 13:35
I think this is a high-quality 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
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M07-28 [#permalink]

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New post 10 Feb 2018, 14:37
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.
M07-28   [#permalink] 10 Feb 2018, 14:37
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