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A dessert recipe calls for 50% melted chocolate and 50% rasp

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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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New post 12 Feb 2020, 16:52
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ScottTargetTestPrep wrote:
vaishnogmat wrote:
A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?

A. 1.5
B. 2.5
C. 3
D. 4.5
E. 5


We are given that a chef makes 15 cups of sauce with 40% melted chocolate, or 15 x 0.4 = 6 cups of melted chocolate, and 60% raspberry puree, or 0.6 x 15 = 9 cups of raspberry puree. We need to determine how many cups of the sauce he needs to remove and replace with pure melted chocolate to make the sauce 50% of each. In order to have 50% of each, we want 7.5 cups of melted chocolate and 7.5 cups of raspberry puree. We can let n = the number of cups of sauce removed and also the number of cups of pure melted chocolate added.

Recall that we have 6 cups of melted chocolate in the sauce (which is 40% of the sauce). If we remove n cups of sauce, we are actually removing 0.4n cups of melted chocolate. Since we are adding back n cups of pure melted chocolate, the number of cups of melted chocolate will increased by n, and we want the end result to be 7.5 cups of melted chocolate. Thus, we can create the following equation to solve for n:

6 - 0.4n + n = 7.5

0.6n = 1.5

n = 1.5/0.6 = 15/6 = 2.5

Answer: B



”We can let n = the number of cups of sauce removed and also the number of cups of pure melted chocolate added.” how can n be both in this case? One is chocolate, the other is mixed. Something is not right.

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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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New post 12 Feb 2020, 17:00
dcummins wrote:
Alternatively

Choc present : 0.4*15 = 6
Puree present: 15-6 = 9

We need to remove a portion of the total mix and replace it with pure choc to get a 1:1 mix as per the instructions.

Represent this as a ratio, letting x be the amount (in weight units) that we remove:
(6-0.4x+x)/(9-0.6x) = 1/1
6+0.6x= 9-0.6x
3=1.2x
x= 30/12
x=5/2 = 2.5

B



Hi Please advise.

If 2.5 cup of the sauce is remove then the remaining is the proportion of 5c of chocolate + 5c of RP. Total cup to be removed = 2.5


Now we need 2.5c of pure chocolate to make up for the removal

Remove-2.5 + add-2.5 = 5 cups total. Isnt this is the case?

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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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New post 12 Feb 2020, 21:29
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David nguyen wrote:
VeritasKarishma wrote:
vaishnogmat wrote:
A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?




A. 1.5
B. 2.5
C. 3
D. 4.5
E. 5


Responding to a pm:

Quote:
Using the Scale method
40% 50% 100%
15-x x
Hence
(15-x)/x = 50/10
I cannot understand how 15- x cups can be equal to 40% of chocolate . where X is the cups of Mixture removed and replaced with Pure Chocolate.

My understanding:
The 15 cups are prepared by mistaken proportions of 40% chocolate and 60% Rasberry . Hence when we remove x cups of mixture from 15 cups of Chocolate + Rasberry Mixture , we are left with chocolate equal to 40% of 15-x
Hence now 40%* ( 15-x) Choco will be mixed with x cups of Choco at 100% to obtain choco at 50%

Is this understanding correct?

Will the concentration of chocolate always be at 40% ,in the 15 Cups prepared by mistaken combination , even if we consider 1 cup or 2 cups or x cups of the mixture?


Yes, we assume that the mix is homogeneous. Otherwise, we will not be able to solve the question.

Look at the question from a different perspective for ease (don't mix it up with algebra):

You have 15 cups of sauce with 40% chocolate. You also have unlimited amount of pure chocolate sauce. Now you need to mix these two in such a way that you get total 15 cups of sauce with 50% chocolate.

Using scale method:

w1/w2 = (100 - 50)/(50 - 40) = 5/1
w1 - Amount of 40% chocolate sauce
w2 - Amount of pure chocolate sauce

So for every 5 cups of 40% chocolate sauce, we need 1 cup of pure chocolate sauce. This will give us 6 cups of 50% chocolate sauce. But we need 15 cups of 50% chocolate sauce.
So we need to mix 5*15/6 = 12.5 cups of 40% chocolate sauce with 1*15/6 = 2.5 cups of pure chocolate sauce.

Hence, when we are replacing, we remove 2.5 cups of 40% chocolate sauce and put 2.5 cups of pure chocolate in it.

Answer (B)

Look at example 1 here: http://www.veritasprep.com/blog/2012/01 ... -mixtures/
It is very similar to this question.



Why is w1 equal to 100?

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w1 is not 100. We need to find w1/w2.
The percentage of chocolate in pure chocolate is 100. That is our A2.
A1 is 40, the percentage of chocolate in our sauce.
Aavg is 50, the required percentage of chocolate in the new mix.

Here is the link to this concept on the Veritas website:
https://www.veritasprep.com/blog/2011/0 ... -averages/
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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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New post 14 Feb 2020, 09:41
David nguyen wrote:

”We can let n = the number of cups of sauce removed and also the number of cups of pure melted chocolate added.” how can n be both in this case? One is chocolate, the other is mixed. Something is not right.

Posted from my mobile device


According to the question stem, we should remove some of the sauce (chocolate and raspberry puree mixed) and replace it with an equal amount of pure chocolate. We need to determine this amount. Thus, if n is the number of cups of sauce removed; then the amount of pure chocolate added is also n. I don't see anything wrong with this part of the solution.

Maybe you are thinking that the amount of chocolate that is in the part of the sauce that we remove and the amount of chocolate that we add back should be equal; however, that is not the case. It would be a very different question if that was the case.
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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp   [#permalink] 14 Feb 2020, 09:41

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