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# How many gallons of milk that is 10 percent butter-fat must

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Director
Joined: 29 Nov 2012
Posts: 775
How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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03 Sep 2013, 06:35
6
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Difficulty:

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?

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

Please provide detailed explanations!

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Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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03 Sep 2013, 06:39
5
1
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.

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Director
Joined: 29 Nov 2012
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Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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03 Sep 2013, 06:44
I Messed up the equations. Thanks for the quick reply!
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Manager
Joined: 23 May 2013
Posts: 108
Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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19 Jan 2014, 06:30
would this be a 600-700 question?
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Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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19 Jan 2014, 09:55
ankur1901 wrote:
would this be a 600-700 question?

I'd say at max a 600-level.
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Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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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.

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?
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Joined: 05 Feb 2014
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Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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09 May 2014, 12:23
2
For guys looking to solve by allegation

10% ............... 35%

........... 20% ..........

15% ................ 10%

$$15/10 = 3/2$$ ->> $$3/2 * 8 = 12$$
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Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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15 Dec 2014, 05:17
Where can allegation concepts be learnt?It seems easier and faster than setting up equations..
Director
Joined: 23 Jan 2013
Posts: 576
Schools: Cambridge'16
Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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14 Mar 2015, 03:53
10%-------------20%-----------35%

10x=15*8

10x=120 => x=12

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Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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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

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Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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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

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Re: How many gallons of milk that is 10 percent butter-fat must  [#permalink]

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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

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Re: How many gallons of milk that is 10 percent butter-fat must &nbs [#permalink] 21 Mar 2018, 16:19
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# How many gallons of milk that is 10 percent butter-fat must

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