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Milk and cream are combined to make a 60-liter mixture that is 50 perc
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22 May 2020, 11:01
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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?
Milk and cream are combined to make a 60-liter mixture that is 50 perc
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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
PS20433
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
Re: Milk and cream are combined to make a 60-liter mixture that is 50 perc
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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.
Milk and cream are combined to make a 60-liter mixture that is 50 perc
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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?
Re: Milk and cream are combined to make a 60-liter mixture that is 50 perc
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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)
Re: Milk and cream are combined to make a 60-liter mixture that is 50 perc
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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!
Re: Milk and cream are combined to make a 60-liter mixture that is 50 perc
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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