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A dessert recipe calls for 50% melted chocolate and 50% rasp 21 May 2016, 11:57
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let x=number of cups to be removed/replaced
15(.4)-x(.4)+x=15(.5)
x=2.5 cups
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A dessert recipe calls for 50% melted chocolate and 50% rasp 22 May 2016, 22:15
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Responding to a pm:

Quote:

Why does it have to be 50 = 60[(15-x)/15] ?

i.e the initial Volume is 15 not 15-x?
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We assume that he removes x cups.

Our formula is based on the concept that amount of raspberry puree does not change in the step.
Initial amount = Final amount
CiVi = CfVf

Think about it: when does the amount of raspberry puree remain same?
When you have 15 cups of mix, there is a certain amount of raspberry puree in it. When you remove x cups, the amount of raspberry puree reduces. You have 15 - x cups of mix now. Now when you add chocolate, the amount of raspberry puree stays the same. So we are applying the concept of "amount stays same" to the "adding chocolate" step only. Before we add chocolate, we have 15-x cups of mix. After we add chocolate, we have 15 cups of mix. Hence, initial volume is 15 - x. Does this help?
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A dessert recipe calls for 50% melted chocolate and 50% rasp 17 May 2017, 17:57
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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
Show more

We've got 9 cups of raspberry and 6 of chocolate. To fix this, we need to remove 1.5 cups of raspberry.

But! We can't take out raspberry by itself. It's already mixed with the chocolate. We can only remove the mix.

Mix = 60% raspberry, 40% chocolate

Every cup of mix we remove = 0.6 cups raspberry + 0.4 cups chocolate

60% of 1 cup = 0.6 cups

So each cup of mix gets us 0.6 cups raspberry

0.6 cups of raspberry * (# of cups of mix) = 1.5 cups of raspberry

0.6 * x = 1.5

x = 2.5

We need 1.5 cups raspberry 0.6 * 2.5 = 1.5

So we need to remove 2.5 cups of mix.

Answer : B
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A dessert recipe calls for 50% melted chocolate and 50% rasp 22 May 2017, 18:40
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vaishnogmat
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
Show more

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
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A dessert recipe calls for 50% melted chocolate and 50% rasp 12 Jan 2018, 13:36
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Hi All,

This question can be solved by TESTing THE ANSWERS.

To start, we're told that 15 cups of 'sauce' are made up of 40% chocolate and 60% raspberry. This gives us...

Total = 15 cups
Choc = 40%(15) = 6 cups
Rasp = 60%(15) = 9 cups

We're told to remove a certain amount of the mixture and replace it with PURE chocolate, so that the mixture becomes a 50/50 chocolate/raspberry mix. In simple terms, we need the total amount of Chocolate to be 7.5 CUPS. We're asked for the number of cups of the mixture that would have to be replaced. Let's TEST THE ANSWERS.

While it's mathematically advantageous to TEST answer B or D first, Answer C seems like easier math...

IF... we remove 3 cups of sauce, those 3 cups are....
40%(3) = 1.2 cups Choc
60%(3) = 1.8 cups Rasp

The number of cups of Choc can be calculated by using the original number of cups (6), subtracting the amount removed when we remove the sauce (in this case, 1.2), then adding back the pure chocolate that replaces the removed sauce (in this case, 3) = 6 - 1.2 + 3 = 7.8 cups chocolate. This is TOO MUCH chocolate (we wanted it to be 7.5 cups), but it's fairly close, so we're likely looking for an answer that is CLOSE to 3....Let's TEST Answer B...

IF... we remove 2.5 cups of sauce, those 2.5 cups are....
40%(2.5) = 1 cup Choc
60%(2.5) = 1.5 cups Rasp

Choc = 6 - 1 + 2.5 = 7.5 cups chocolate. This is EXACTLY what we're looking for, so this MUST be the answer.

Final Answer:
Show Spoiler
B


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A dessert recipe calls for 50% melted chocolate and 50% rasp 12 Nov 2018, 04:30
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Quote:
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
Show more

Current volume = 15 cups

Melted chocolate present as of now = 40% of 15 = 6 cups
raspberry Puree present as of now = 60% of 15 = 9 cups

Let, the volume replaced = x cups
raspberry Puree present in x cups = 60% of x = 0.6x cups
Since the x cups are being replaced by Pure melted chocolate so the raspberry puree that goes does will NOT come back

i.e. Net value of Raspberry puree after replacement of x cups by melted chocolate = 9 - 0.6x (which should make it 50% of the entire solution as desired)

i.e. 9 - 0.6x = 50% of 15 cups = 7.5 cups

i.e. 0.6x = 9 - 7.5 = 1.5 cups

i.e. x = 2.5 cups

Answer: Option B
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A dessert recipe calls for 50% melted chocolate and 50% rasp 06 Dec 2018, 04:19
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vaishnogmat
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
Show more

Quote:

How can this problem be solved by concentration method?
the amount of raspberry puree remains constant:
Ci x Vi = Cf x Vf
3/5 x 15 = 1/2 x (15-x)
x = 3
what am i missing?
Show more

Say you remove x cups from the total 15 cups. So volume of sauce before you add more melted chocolate is (15 - x) cups. The volume of sauce after you add melted chocolate is 15 cups again.
The amount of raspberry puree before and after this step of adding back remains the same. So,

Ci x Vi = Cf x Vf
60 * (15 - x) = 50 * (15)
x = 150/60 = 2.5 cups

Answer (B)

Note that we use CiVi = CfVf after removing a part of the mix.
Weight = Concentration*Volume
The weight of raspberries remains the same before adding back x cups and after adding back x cups. So those two points are your initial and final points.
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A dessert recipe calls for 50% melted chocolate and 50% rasp 21 Mar 2019, 14:04
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vaishnogmat
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
Show more
\(?\,\,\, = \,\,\,x = \# \,\,{\rm{out}}\,\,\underline {{\rm{sauce}}} \,\,{\rm{cups}}\,\, = \,\,\# \,\,{\rm{in}}\,\,\underline {{\rm{100\% }}\,\,{\rm{choco}}} \,\,{\rm{cups}}\)

\(\matrix{\\
{{\rm{real}} \to {\rm{ideal}}} \cr \\
{15\,\,{\rm{cups}}} \cr \\
\\
} \,\,\,\left\{ \matrix{\\
\,{\rm{choco}}\,:\,\,{2 \over 5}\left( {15} \right)\,\,{\rm{cups}} - x \cdot {2 \over 5}\,\,{\rm{cups}} + x\,\,{\rm{cups}}\,\,\,\,\, = \,\,\,\,{{2.5} \over 5}\left( {15} \right)\,\,{\rm{cups}} \hfill \cr \\
\,{\rm{rasp}}\,:\,\,{3 \over 5}\left( {15} \right)\,\,{\rm{cups}} - x \cdot {3 \over 5}\,\,{\rm{cups}} + 0\,\,{\rm{cups}}\,\,\,\,\, = \,\,\,\,{{2.5} \over 5}\left( {15} \right)\,\,{\rm{cups}} \hfill \cr} \right.\)

\({3 \over 5}\left( {15} \right)\,\,{\rm{cups}} - x \cdot {3 \over 5}\,\,{\rm{cups}}\,\,\,\,\, = \,\,\,\,{{2.5} \over 5}\left( {15} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{3 \over 5}x = {{0.5} \over 5}\left( {15} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = 2.5\)

\(\left[ {\,{2 \over 5}\left( {15} \right)\,\,{\rm{cups}} - x \cdot {2 \over 5}\,\,{\rm{cups}} + x\,\,{\rm{cups}}\,\,\,\,\, = \,\,\,\,{{2.5} \over 5}\left( {15} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{3 \over 5}x = {{0.5} \over 5}\left( {15} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = 2.5} \right]\)


The correct answer is (B).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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A dessert recipe calls for 50% melted chocolate and 50% rasp Updated on: 05 Oct 2022, 22:35
Originally posted by KarishmaB on 13 May 2019, 03:27.
Last edited by KarishmaB on 05 Oct 2022, 22:35, edited 1 time in total.
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vaishnogmat
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
Show more

Quote:

I am just not able to get my head around this question and its answer. I am getting 3 as the answer, and I am not able to understand any of the explanations.

Could you please help me out on this one?

Show more

You are removing a bit of the sauce and adding pure chocolate instead.
This is similar to mixing some part of 40% sauce with pure chocolate (100% chocolate) so we can use our standard mixture formula. The mix should be done in a way that you get 50% chocolate sauce.

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.
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A dessert recipe calls for 50% melted chocolate and 50% rasp 12 Feb 2020, 17:41
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vaishnogmat
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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/01 ... -mixtures/
It is very similar to this question.
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Why is w1 equal to 100?

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A dessert recipe calls for 50% melted chocolate and 50% rasp 12 Feb 2020, 17:52
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vaishnogmat
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
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”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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A dessert recipe calls for 50% melted chocolate and 50% rasp Updated on: 05 Oct 2022, 22:47
Originally posted by KarishmaB on 12 Feb 2020, 22:29.
Last edited by KarishmaB on 05 Oct 2022, 22:47, edited 1 time in total.
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vaishnogmat
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)



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.
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A dessert recipe calls for 50% melted chocolate and 50% rasp 14 Feb 2020, 10:41
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”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
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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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A dessert recipe calls for 50% melted chocolate and 50% rasp 04 Jul 2020, 03:27
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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
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Chocolate percentage in the incorrect sauce: 40%.
Chocolate percentage in the pure chocolate: 100%.
Chocolate percentage in the mixture: 50%.

Let I = the incorrect sauce and C = the pure chocolate.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for I and C on the ends and the percentage for the mixture in the middle.
I 40%----------50%-----------100% C

Step 2: Calculate the distances between the percentages.
I 40%----10----50%----50-----100% C

Step 3: Determine the ratio in the mixture.
The ratio of I to C is equal to the RECIPROCAL of the distances in red.
I:C = 50:10 = 5:1.

Since I:C = (5 cups) : (1 cup), 1 of every 6 cups must be pure chocolate.
Thus:
Pure chocolate = (1/6)(15 cups) = 15/6 = 5/2 = 2.5 cups.

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rsrighosh
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A dessert recipe calls for 50% melted chocolate and 50% rasp 27 Sep 2020, 05:36
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I used the replacement theory described here
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/01 ... -mixtures/

Note that in the entire replacement process,
a) Mixture is homogenous (as its all liquid)
b) Quantity of raspberry puree is untouched (constant) => 60% in 15 cups will be changed to 50% after x cups of solution is replaced by pure melted chocolate
c) quantity of melted chocolate is varying (melted chocolate is being added to correct the concentration)

Hence going by the replacement formula,
we have to go by the raspberry puree (constant)

x is the no. of cups removed

Ci*Vi = Cf*Vf
\(\frac{60}{100}(15-x) = \frac{50}{100} (15)\)
or \(6(15-x) = 5(15)\)
or \(x= 2.5\)
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A dessert recipe calls for 50% melted chocolate and 50% rasp 28 Sep 2020, 23:14
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rsrighosh
I used the replacement theory described here
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/01 ... -mixtures/

Note that in the entire replacement process,
a) Mixture is homogenous (as its all liquid)
b) Quantity of raspberry puree is untouched (constant) => 60% in 15 cups will be changed to 50% after x cups of solution is replaced by pure melted chocolate
c) quantity of melted chocolate is varying (melted chocolate is being added to correct the concentration)

Hence going by the replacement formula,
we have to go by the raspberry puree (constant)

x is the no. of cups removed

Ci*Vi = Cf*Vf
\(\frac{60}{100}(15-x) = \frac{50}{100} (15)\)
or \(6(15-x) = 5(15)\)
or \(x= 2.5\)
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Yes, it is applicable and as you seem to have figured out, you need to work with the percentages of raspberry, not chocolate. Since chocolate is added, its amount will increase. The thing whose amount remains the same after removing and after adding back is raspberry puree.
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A dessert recipe calls for 50% melted chocolate and 50% rasp 11 Nov 2020, 23:54
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Total quantity= 15 cups
Requirement= 50% (7.5 cups) chocolate & 50 % (7.5 cups) puree

Currently 6 cups (40% of 15 cups) is chocolate

Differance of 1 cup chocolate replacement: 1 - 0.4 = 0.6 cups Chocolate

Chocolate to be replaced: 7.5 - 6 = 1.5 cups

Equation is \(\frac{1.5}{0.6}\) = 2.5 cups

No need to remember any equation (only understand the logic)
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A dessert recipe calls for 50% melted chocolate and 50% rasp 28 Jun 2022, 05:14
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The raspberry content in 15 cups = 15*60/100 = 9 cups.
Thus melted chocolate= 15 - 9 = 6 cups

Let the baker remove x cups of sauce and add the same amount of melted chocolate.

6 - 0.4x + x = 50% of 15
0.6x = 7.5 - 6
x = 2.5

Thus, the correct option is B.
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A dessert recipe calls for 50% melted chocolate and 50% rasp 29 Jun 2022, 11:54
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Instead of complicated calculations, we can assume values here
let each cup be 10 ml and 15 cups so will be 150 ml. (this is the sauce that has been prepared)
We need to have 75 ml of both sauces.(ratio 50:50)
Now the present ratio is 60:40 between raspberry and chocolate sauce.
that works out as 90 ml of raspberry and 60 ml of chocolate sauce.
Each of the 10 cups will have 6 ml raspberry and 4 ml chocolate when taken out.
therefore from 90 ml to 75 ml of raspberry, we will need to take out (90-75)/6=2.5 cups Ans.(B)
Feel free to correct and always happy to learn.
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A dessert recipe calls for 50% melted chocolate and 50% rasp 18 Aug 2023, 07:54
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Let's break down the problem step by step:

The chef currently has 15 cups of the sauce with the following composition:

40% melted chocolate
60% raspberry puree
The chef wants to adjust this mixture to the proper 50% melted chocolate and 50% raspberry puree mixture.

Let's assume the chef needs to remove and replace "x" cups of the sauce with pure melted chocolate. After the replacement, the total volume of the sauce remains 15 cups.

When "x" cups of the sauce are removed and replaced with pure melted chocolate, the composition of the sauce becomes:

(15 - x) cups * 40% melted chocolate
(15 - x) cups * 60% raspberry puree
The new mixture should be 50% melted chocolate and 50% raspberry puree. This can be represented by the equation:

0.40 * (15 - x) + 1.00 * x = 0.50 * 15

Solving for "x":

0.40 * (15 - x) + x = 7.5
6 - 0.40x + x = 7.5
0.60x = 1.5
x = 1.5 / 0.60
x = 2.5

So, the chef needs to remove and replace 2.5 cups of the sauce with pure melted chocolate to achieve the proper 50% melted chocolate and 50% raspberry puree mixture.

The correct answer is:

B. 2.5
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