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A snack mix that is 20% raisins is blended with a second mix that is

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A snack mix that is 20% raisins is blended with a second mix that is  [#permalink]

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New post 18 Jan 2017, 10:42
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A snack mix that is 20% raisins is blended with a second mix that is 30% raisins. The initial blend is 5 pounds of the first mix and 10 pound of the second. To make the final blend 22% raisins, how many additional pounds of the first mix must be added to the initial blend?

A - 25
B - 30
C - 35
D - 40
E - 50


Is it possible to use "alligation method" here?
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Re: A snack mix that is 20% raisins is blended with a second mix that is  [#permalink]

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New post 19 Jan 2017, 02:39
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Before I jump in to solve this question, let me provide you a brief explanation of how to approach weighted average questions on the GMAT. Weighted average questions can be easily solved by making use of the alligation/mixture diagram given below.

Attachment:
Mixtures 1.png
Mixtures 1.png [ 8.12 KiB | Viewed 1916 times ]


Putting in values in the alligation/mixture diagram and subtracting along the diagonals gives us a ratio in which two quantities are mixed. This ratio can now be used to find out what specific amounts of two quantities need to be mixed to obtain a particular mixture.

The only thing that you need to keep in mind here is that the values you need to use, that is the higher value, lower value and mean value have to be values which are associated with the word 'per' (percents, average, per km, per kg etc.).

The alligation/mixture diagram proves useful not only when mixing solutions or combining solids but also to explain the weighted average concept (the word average is also associated with the word per i.e. if the average marks of the class is 80, then it can be understood as 80 marks per student). Say if we have a class A where the average marks is 80 and another class B where the average marks is 70 and the combined average of both class A and B is 74, then we can definitely comment upon which class has the greater number of students. If we represent the average values in the mixture diagram, the ratio of students of Class A and Class B will be 2 : 3. This clearly indicates that class B has the greater number of students.

Now this alligation/mixture diagram can also be used in the above question, since we are mixing two percentages. So creating the alligation/mixture diagram for the percentage of raisins we get

Attachment:
Mixtures 2.png
Mixtures 2.png [ 7.51 KiB | Viewed 1915 times ]


Now since the ratio of the second mix to the first mix has to be 1 : 4, and since the 2nd mix is 10 pounds raisins we need 40 pounds of the 1st mix. This means we will require an additional 35 pounds of the first mix.

Hope this helps!

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Re: A snack mix that is 20% raisins is blended with a second mix that is  [#permalink]

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New post 18 Jan 2017, 11:42
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Jeoren wrote:
A snack mix that is 20% raisins is blended with a second mix that is 30% raisins. The initial blend is 5 pounds of the first mix and 10 pound of the second. To make the final blend 22% raisins, how many additional pounds of the first mix must be added to the initial blend?

A - 25
B - 30
C - 35
D - 40
E - 50


Is it possible to use "alligation method" here?


let x=additional pounds of first mix to be added
.2*(5+x)+.3*10=.22*(15+x)
x=35 pounds
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Re: A snack mix that is 20% raisins is blended with a second mix that is  [#permalink]

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New post 19 Jan 2017, 04:11
22% is closer to 20% ( Mix 1) than 30% Mix 2 , so we will have more mix 1 than mix 2.

20% ( +2) 22% ( + 8) 30%

so 8 portion of mix 1 is mixed with 2 portion of mix 2

2 portion = 10 pound ( mix 2 = 10 pound)
1 portion = 5 pound

8 portion = 40 pound

so we need 40 pound of mix 1 , since 5 pound of mix 1 is already mixed, 35 pound more of mix1 needs to be mixed
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Re: A snack mix that is 20% raisins is blended with a second mix that is  [#permalink]

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New post 16 Aug 2017, 22:35
Jeoren wrote:
A snack mix that is 20% raisins is blended with a second mix that is 30% raisins. The initial blend is 5 pounds of the first mix and 10 pound of the second. To make the final blend 22% raisins, how many additional pounds of the first mix must be added to the initial blend?

A - 25
B - 30
C - 35
D - 40
E - 50


Is it possible to use "alligation method" here?



Let first mix to be added be "X".

20 30
22
8 : 2
4 : 1

4/1=5+X/10
X=35

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Re: A snack mix that is 20% raisins is blended with a second mix that is  [#permalink]

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New post 17 Aug 2017, 05:13
Ans is 35pounds C

let mix 1 is used x pounds and raisins will be .2x
mix 2 used is 10 pounds and raisins are 3 pounds
total mix is x+10

.2x+3 = 0.22(x+10)
x=40
hence we should have used 40 pounds to get 22% raisins, but we already used 5 hence 35 more to be used...
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Re: A snack mix that is 20% raisins is blended with a second mix that is  [#permalink]

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New post 20 Aug 2017, 07:10
Using allegation :

20........22............30

w1/w2=(30-22)/(22-20)=8/2=4/1

Therefore for for 1 part of second mix and 4 parts of 1st mix give 22% solution.

Since 2nd mix is 10gms, 1st mix needs to be 40gms to give 22% soln.

Hence extra gms of 1st mix needed are = 40-5=35gms

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Re: A snack mix that is 20% raisins is blended with a second mix that is  [#permalink]

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New post 12 Oct 2018, 07:02
Jeoren wrote:
A snack mix that is 20% raisins is blended with a second mix that is 30% raisins. The initial blend is 5 pounds of the first mix and 10 pound of the second. To make the final blend 22% raisins, how many additional pounds of the first mix must be added to the initial blend?

A - 25
B - 30
C - 35
D - 40
E - 50


The first mix has 5 x 0.2 = 1 lb of raisins and the second mix has 10 x 0.3 = 3 lb of raisins. If we let x = the additional number of pounds of the first mix that must be added to the initial blend to produce a blend of 22% raisins, then we have:

(1 + 3 + 0.2x)/(5 + 10 + x) = 22/100

100(4 + 0.2x) = 22(15 + x)

400 + 20x = 330 + 22x

70 = 2x

35 = x

Answer: C
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Re: A snack mix that is 20% raisins is blended with a second mix that is  [#permalink]

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New post 12 Oct 2018, 12:01
Jeoren wrote:
A snack mix that is 20% raisins is blended with a second mix that is 30% raisins. The initial blend is 5 pounds of the first mix and 10 pound of the second. To make the final blend 22% raisins, how many additional pounds of the first mix must be added to the initial blend?

A - 25
B - 30
C - 35
D - 40
E - 50


Is it possible to use "alligation method" here?

\(? = x\)

Let me show you the GMATH´s way of dealing with Alligation (and Bruce Lee):

Image

\(\frac{{10}}{{10 + \left( {5 + x} \right)}} = \frac{{22 - 20}}{{30 - 20}} = \frac{{2 \cdot \boxed5}}{{10 \cdot \boxed5}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,15 + x = 50\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,? = x = 35\,\,\,\,\,\,\,\,\left[ {{\text{pounds}}} \right]\,\,\,\,\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: A snack mix that is 20% raisins is blended with a second mix that is   [#permalink] 12 Oct 2018, 12:01
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