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Milk and cream are combined to make a 60-liter mixture that is 50 perc

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Milk and cream are combined to make a 60-liter mixture that is 50 perc  [#permalink]

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New post 22 May 2020, 11:01
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Re: Milk and cream are combined to make a 60-liter mixture that is 50 perc  [#permalink]

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New post 23 May 2020, 14:17
1
B?
Milk =x
Cream = 60-x

5x/100 + 75(60-x)/100 = 30

Solving: x = 150/7 = 21.xx
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Milk and cream are combined to make a 60-liter mixture that is 50 perc  [#permalink]

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New post Updated on: 23 May 2020, 04:58
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Bunuel wrote:
Milk and cream are combined to make a 60-liter mixture that is 50 percent butterfat. If the milk is 5 percent butterfat and the cream is 75 percent butterfat, approximately how many liters of milk are in the mixture?

A. 20.00
B. 21.43
C. 30.00
D. 38.57
E. 42.75

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Looks like a perfect opportunity to use weighted averages
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let x = the number of liters of MILK needed in the mixture
So, the PROPORTION of milk in the mixture = x/60 [since we have a total of 60 liters in the final mixture]

Since we have a total of 60 liters in the mixture, 60 - x = the number of liters of CREAM needed in the mixture
So, the PROPORTION of cream in the mixture = (60 - x)/60

We want the resulting mixture to contain 50% butterfat

Plug all of these values into the equation to get: 50 = (x/60)(5) + ((60 - x)/60)(75)
Multiply both sides by 60 to get: 3000 = (5)(x) + (60 - x)(75)
Expand: 3000 = 5x + 4500 - 75x
Simplify: 3000 = 4500 - 70x
Subtract 4500 from both sides: -1500 = -70x
Solve: x = (-1500)/(-70) = (1500)/(70) = 150/7

If you'd rather not divide 150 by 7, you can quickly evaluate this by first recognizing that 140/7 = 20
So, 150/7 must be a little bit bigger than 20

Answer: B

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Originally posted by BrentGMATPrepNow on 22 May 2020, 17:07.
Last edited by BrentGMATPrepNow on 23 May 2020, 04:58, edited 1 time in total.
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Re: Milk and cream are combined to make a 60-liter mixture that is 50 perc  [#permalink]

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New post 22 May 2020, 20:59
Use options.
Milk content will have 5% butter fat.
Total content is 60
So, 60-milk = cream

Now,
A) 20 is milk
40 will be cream.
=> 20*5/100= 1litre of butterfat
=> 40*75/100 = 30 litre of butterfat
---------------------------
Total 31 litre of butterfat (greater than 50% of 60 litre of mixture)

(So it has to be slightier bigger than 20litre of milk)

B) 21.43 is milk
60-21.43 = 38.57 is creame
=> 21.43*5/100= 1.0715 litre of butterfat.
=> 38.57*75/100= 28.9275 litre of butterfat.
---------------------------
Total butterfat is 1.0715+28.9275=30 ( desired result, 50% of 60 litre of mixture)

We can stop here, because we already got answer but if you want to check, you can check rest with the similar approach.

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Milk and cream are combined to make a 60-liter mixture that is 50 perc  [#permalink]

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New post 23 May 2020, 03:55
Quote:
Looks like a perfect opportunity to use weighted averages
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let x = the number of liters of MILK needed in the mixture
So, the PROPORTION of milk in the mixture = x/60 [since we have a total of 60 liters in the final mixture]

Since we have a total of 60 liters in the mixture, 60 - x = the number of liters of CREAM needed in the mixture
So, the PROPORTION of milk in the mixture = (60 - x)/60
We want the resulting mixture to contain 50% butterfat

Plug all of these values into the equation to get: 50 = (x/60)(5) + ((60 - x)/60)(75)
Multiply both sides by 60 to get: 3000 = (5)(x) + (60 - x)(75)
Expand: 3000 = 5x + 4500 - 75x
Simplify: 3000 = 4500 - 70x
Subtract 4500 from both sides: -1500 = -70x
Solve: x = (-1500)/(-70) = (1500)/(70) = 150/7

If you'd rather not divide 150 by 7, you can quickly evaluate this by first recognizing that 140/7 = 20
So, 150/7 must be a little bit bigger than 20

Answer: B


Thank you BrentGMATPrepNow for your explanation! I have some questions...
1. Shouldn't milk (marked in bold above) be cream? If not, why?
2. I am confused why you use 50 and not 30(L) in the equation (I understand you get the 50 from the 50% ratio). Does it has to do with the fact that we are only using proportions and percentages in the equation? If that is true, why are we not using 1/2 instead of 50?

Please let me know! :)
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Re: Milk and cream are combined to make a 60-liter mixture that is 50 perc  [#permalink]

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New post 23 May 2020, 05:02
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WBogey wrote:
Thank you BrentGMATPrepNow for your explanation! I have some questions...
1. Shouldn't milk (marked in bold above) be cream? If not, why?
2. I am confused why you use 50 and not 30(L) in the equation (I understand you get the 50 from the 50% ratio). Does it has to do with the fact that we are only using proportions and percentages in the equation? If that is true, why are we not using 1/2 instead of 50?

Please let me know! :)


1. Thanks for catching that. Yes, it should be cream. I have edited my response accordingly.

2. I'm not sure where the 30 comes in.
You can think of this as combining two groups: Milk and Cream.
Each group has a certain percentage of butterfat. Milk is 5% butterfat, and cream is 75% butterfat,
We want the combined mixture to contain 60 liters, and we want that mixture to be 50% butterfat (that's where I got the 50 from)

Does that help?
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Re: Milk and cream are combined to make a 60-liter mixture that is 50 perc  [#permalink]

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New post 23 May 2020, 07:10
BrentGMATPrepNow wrote:
WBogey wrote:
Thank you BrentGMATPrepNow for your explanation! I have some questions...
1. Shouldn't milk (marked in bold above) be cream? If not, why?
2. I am confused why you use 50 and not 30(L) in the equation (I understand you get the 50 from the 50% ratio). Does it has to do with the fact that we are only using proportions and percentages in the equation? If that is true, why are we not using 1/2 instead of 50?

Please let me know! :)


1. Thanks for catching that. Yes, it should be cream. I have edited my response accordingly.

2. I'm not sure where the 30 comes in.
You can think of this as combining two groups: Milk and Cream.
Each group has a certain percentage of butterfat. Milk is 5% butterfat, and cream is 75% butterfat,
We want the combined mixture to contain 60 liters, and we want that mixture to be 50% butterfat (that's where I got the 50 from)

Does that help?


That makes sense! FYI: The 30 comes from the 50% ratio of butterfat in the 60L mixture (which is 30L). I got confused and mixed two formulas. I just have to get used to the weighted average formula! Again thanks!
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Re: Milk and cream are combined to make a 60-liter mixture that is 50 perc  [#permalink]

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New post 30 May 2020, 21:16

Solution



Given
In this question, we are given that
• Milk and cream are combined to make a 60-liter mixture that is 50 percent butterfat
• Milk is 5 percent butterfat and the cream is 75 percent butterfat

To find
We need to determine
• The number of litres of milk are in the mixture

Approach and Working out
Let x be the number of litres of milk in the mixture, and y be the number of litres of cream
    • \((\frac{5}{100})x + (\frac{75}{100})y = 30\)
      o 5x +75y = 3000
      o x + 15y = 600
      o And, we know x + y = 60

    • Thus, 14x = 300
      o Implies, \(x = \frac{150}{7} = 21.43\)

Thus, option B is the correct answer.

Correct Answer: Option B
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Re: Milk and cream are combined to make a 60-liter mixture that is 50 perc   [#permalink] 30 May 2020, 21:16

Milk and cream are combined to make a 60-liter mixture that is 50 perc

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