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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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07 Nov 2014, 15:37
blueseas wrote:
vaishnogmat wrote:
Q) 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 have 15 cups os sauce with $$40 %$$ choc and $$60 %$$ rasb
cups of choc = $$0.4*15 = 6$$
cups of rasb = $$0.6*15 = 9$$
now let say we removed x cup of original mix and replaced with x cups of choc.
therefore final number of cups of choc =$$6-0.4x+x$$
now this number of cup should be 50% of total = $$15/2 = 7.5$$
therefore $$6-0.4x+x= 7.5$$
on solving $$x= 2.5$$

hence B

Hi,
I was with you until " final number of cups of choc =$$6-0.4x+x$$"

After I came up with 6 and 9, i proceeded to divide the options in half. What I mean is, for option B, 2.5 -- if we removed 2.5, that means that we would remove half of the 2.5 = 1.25 of chocolate and 1.25 of puree. I'm not sure why you removed 40%(although I can see that 40% represents the chocolate percent). Logically, if we remove the sauce, wouldn't we remove equal parts of puree and equal parts of chocolate?
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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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21 Dec 2015, 23:46
The key is to think that the removed cups will remove the 40% chocolate as well.
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A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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Updated on: 11 Nov 2018, 13:26
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

let x=cups of sauce to be removed/replaced
.4*15-.4x+x=.5*15
x=2.5 cups
B

Originally posted by gracie on 23 Dec 2015, 14:14.
Last edited by gracie on 11 Nov 2018, 13:26, edited 2 times in total.
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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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20 May 2016, 11:19
Can someone please explain if the quantity of Raspberry in the original (faulty) and the final mixture will remain the same? Since we are only adding Chocolate?
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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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21 May 2016, 00:31
powellmittra wrote:
Can someone please explain if the quantity of Raspberry in the original (faulty) and the final mixture will remain the same? Since we are only adding Chocolate?

No. He is going to remove the sauce (mix of chocolate and raspberry) and then add more chocolate to it. So the initial amount of raspberry is not the same as the final amount. But after the removal process, he adds only chocolate so yes, in that step, the amount of raspberry does not change.

Check here for the complete solution: a-dessert-recipe-calls-for-50-melted-chocolate-and-50-rasp-158248.html#p1376400
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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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

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22 May 2016, 22:15
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?

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

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22 May 2017, 18:40
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

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

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12 Jan 2018, 13:36
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.

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

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11 Nov 2018, 12:34
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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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06 Dec 2018, 04:19
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

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?

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

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

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21 Mar 2019, 14:04
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

$$?\,\,\, = \,\,\,x = \# \,\,{\rm{out}}\,\,\underline {{\rm{sauce}}} \,\,{\rm{cups}}\,\, = \,\,\# \,\,{\rm{in}}\,\,\underline {{\rm{100\% }}\,\,{\rm{choco}}} \,\,{\rm{cups}}$$

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

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

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

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

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

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29 Mar 2019, 22:47
summer101 wrote:
I misread the question, Again!! Nyways another method
40% 50%
\ /
50%
/ \
100% 10%

so 50/10 = 15-x/x => x =2.5 cups

I think I am not aware of basic working in this method, I can understand the 10% (weight) on the right bottom, But can someone please explain how the weight of melted chocolate is 100% (Left bottom).
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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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06 Apr 2019, 08:42
can this be solved with criss cross method?
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A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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10 Apr 2019, 18:12
one cup has 3/5 amount of rasp. from that we are removing x amount of sauce. Thereby effectively removing 3x/5 amount of sauce; inorder to obtain 1/2 amount of rasp. Now applying this directly we have 3/5 - 3x/5 = 1/2 ===> x = 1/6

For 15 cups ==> x = 15*1/6 ==> 2.5 cups
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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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07 May 2019, 01:32
Bunuel 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

Similar questions to practice:
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Hope it helps.

@Buneul, please help me on the following statement. A solution in one of GMAT Prep books is thus.

With 15 cups at 40%:60% mixture, you have 6 cups of melted chocolate and 9 cups of Raspberry juice. Adding 3 cups of chocolate would give an even amount of each, but remember we are removing an equivalent amount of original mixture. Thus we need to remove and replace fewer than 3 cups. So C, D and E options are eliminated.

I followed the first sentence, but couldn't understand why one needs to remove fewer than 3 cups. Please offer a conceptual understanding.
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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp  [#permalink]

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13 May 2019, 03:27
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

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.

Please check the first part of this post first: https://www.veritasprep.com/blog/2012/0 ... -mixtures/

This question is similar to Question 1 discussed in the post. 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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Re: A dessert recipe calls for 50% melted chocolate and 50% rasp   [#permalink] 13 May 2019, 03:27

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