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

Question

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!

Bunuel · Accepted Answer

Equate the fat:

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

Answer: B.

BrentGMATPrepNow · Answer

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

Answer: B

RELATED VIDEO
 https://www.youtube.com/watch?v=7Or9gzROsjQ

fozzzy · Answer

I Messed up the equations. Thanks for the quick reply!

ankur1901 · Answer

would this be a 600-700 question?

Bunuel · Answer

I'd say at max a 600-level.

yagobert · Answer

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?

gauravsoni · Answer

For guys looking to solve by allegation

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

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

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

15/10 = 3/2  ->>  3/2 * 8 = 12

Ralphcuisak · Answer

Where can allegation concepts be learnt?It seems easier and faster than setting up equations..

Temurkhon · Answer

10%-------------20%-----------35%

10x=15*8

10x=120 => x=12

B

GMATinsight · Answer

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

JeffTargetTestPrep · Answer

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

mm229966 · Answer

1st approach:

A/B = (35 - 20)/(20-10) = 15/10 = 3/2; 
3/2 * 8 = 12 gallons

2nd approach:
0.1X + 0.35*8 = 0.2(X+8) => X = 12

3rd approach:
10%____20%________35%
10X = 15*8
10X = 120
X = 12

errorlogger · Answer

https://i.imgur.com/sfA9cWo.jpg  - B!

bumpbot · Answer

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

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