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How many gallons of milk that is 10 percent butter-fat must
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03 Sep 2013, 06:35

6

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A

B

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D

E

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15% (low)

Question Stats:

85% (01:48) correct 15% (02:08) wrong based on 313 sessions

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How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat?

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03 Sep 2013, 06:39

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fozzzy wrote:

How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat?

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24 Jan 2014, 08:03

Bunuel wrote:

fozzzy wrote:

How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat?

a) 6 b) 12 c) 14 d) 16 e) 28

Please provide detailed explanations!

Equate the fat:

0.1x + 0.35*8 = 0.2(x + 8) --> x = 12.

Answer: B.

Thanks. This is so easy with these equations! I was trying to solve this using weighted averages formula and end up with 15:10 = 8:x => x = 4/3 How can this be solved using the weighted average formula?

Re: How many gallons of milk that is 10 percent butter-fat must
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29 Aug 2016, 10:53

fozzzy wrote:

How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat?

a) 6 b) 12 c) 14 d) 16 e) 28

Please provide detailed explanations!

Fat of First Solution + Fat of second Solution = Fat of Final Mixture

(10/100)*x + (35/100)*8 = (20/100)*(x+8)

i.e. 10x + 280 = 20x + 160

i.e. 10x = 120

i.e. x = 12

Answer: Option B
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Re: How many gallons of milk that is 10 percent butter-fat must
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20 Mar 2018, 08:14

Top Contributor

fozzzy wrote:

How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat?

a) 6 b) 12 c) 14 d) 16 e) 28

One option is to focus on the butter fat

We begin with 8 gallons of milk that is 35 percent butter-fat So, the volume of butter fat = 35% of 8 = (0.35)(8) = 2.8 gallons of butter fat (to begin)

Let x = number of gallons of milk that is 10 percent butter-fat to be added to the initial 8 gallons The volume of butter fat = 10% of x = 0.1x gallons of butter fat (to be added)

So, in the RESULTING mixture, we have: Total volume of butter fat = 2.8 + 0.1x TOTAL VOLUME of mixture = 8 + x

We want the RESULTING mixture to be 20 percent butter-fat In other words, we want: (Total volume of butter fat)/(TOTAL VOLUME of mixture) = 20% We can now write: (2.8 + 0.1x)/(8 + x) = 20/100 Cross multiply to get: 100(2.8 + 0.1x) = 20(8 + x) Expand: 280 + 10x = 160 + 20x Rearrange: 120 = 10x Solve: x = 12

Re: How many gallons of milk that is 10 percent butter-fat must
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21 Mar 2018, 16:19

fozzzy wrote:

How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat?

a) 6 b) 12 c) 14 d) 16 e) 28

We add x gallons of 10% butterfat milk to 8 gallons of 35% butterfat milk, and we obtain (x + 8) gallons of 20% butterfat milk. We can express this in an equation as:

0.1x + 0.35(8) = 0.2(x + 8)

0.1x + 2.8 = 0.2x + 1.6

1.2 = 0.1x

12 = x

Answer: B
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