A snack mix that is 20% raisins is blended with a second mix that is 3 : Problem Solving (PS)

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

23 May 2020, 20:16

Answer C
let x be additional pound of first mix
Initial amount of first mix=0.2 * 5=1
Initial amount of 2nd mix=0.3*10=3
Final blend amount=0.22*(5+10+x)
this final blend amount will be equal to (3+1+0.2 *x)
0.22*(5+10+x)=3+1+0.2*x
x=35

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

23 May 2020, 20:40

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Given:
1. A snack mix that is 20% raisins is blended with a second mix that is 30% raisins.
2. The initial blend is 5 pounds of the first mix and 10 pounds of the second. Asked: To make the final blend 22% raisins, how many additional pounds of the first mix must be added to the initial blend?

Raisins = 20%*5 + 30%*10 = 1+3 = 4 pounds
Total mix = 5 + 10 = 15 pounds
Let x pounds of first mix be added to initial blend to make final blend 22% raisins
Raisins = 4 + .2x
Total final blend = 15 + x
Percentage raisins = (4 + .2x)/(15+x) = .22
4 + .2x = 3.3 + .22x; .02x = .7
x = 70/2 = 35

IMO C

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

23 May 2020, 21:39

IMO C

First Mix= 20% raisins
Second mix = 30% raisins
Ratio of first:Second = 5:10 = 1:2
Ratio of raisin in Initial Mix= 1 x 20 + 2 x 30 / (1+2) = 80/3 %

Now refer attached image, ratio of initial mix: first mix to get 22% raisin = (22-20) : (80/3-22) = 2: 14/3

2K = 15
So, 14/3K = 15/2 x 14/3 = 35

So First mix additional = 35

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

23 May 2020, 23:35

5*1/5+10*3/10= 4 pounds of raisin in 15 pounds of mixture that is 26.66% Of total mixture.

Now to make it 22% 9f whole mixture.

X/5+4 = (15+x)*22/100
X = 35

Answer is C

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

24 May 2020, 07:04

Nomenclature, Raisin proportion in snack = R(), First Mix = M1, Second Mix = M2, Initial Blend = I, Final Blend = F
Extra Pound added for Final Blend = Q

R(M1) = 2/10
R(M2) = 3/10

R(I) = [ 5X2/10 + 10X3/10] / 15 = 4/15

R(F) = 22/100 = [ 4 + Q.(2/10) ] / [ 15 + Q ]

Simplyfying both sides, (15 + Q) X 22 = 100 X (4 + 0.2 Q)
330 + 22Q = 400 + 20Q
2Q = 70
Q = 35

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

24 May 2020, 08:29

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 pounds 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

let x=additional pounds added to initial blend
.20(5+x)+.30(10)=.22(15+x)→
x=35 pounds
C

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

24 May 2020, 11:00

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Answer : C

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

24 May 2020, 12:36

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I got C.

20% of 1st Mix + 30% of 2nd Mix ----> 22% of Final Mix , By Alligation method

( 30 - 22) / ( 22 - 20 ) = 8 / 2 = 4 : 1 Ratio of 1st Mix to 2nd Mix
Given , 2nd Mix in final ratio = 10 Pounds , So 1st mix = 4x10 = 40 Pounds

Initial 1st Mix Qty available = 5 pounds, so 40 - 5 = 35 Pounds of first Mix is Required in the final Mix.

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

24 May 2020, 13:41

Ans is C
If we add another 35 pounds of first mixture then the ratio in which two mixtures are mixed will be 4:1
Now in 1st mixture 2:8 is ratio
And in 2nf mixture 3:7 is ratio
As they are mixed in 4:1
So first rstio becomes 8:32
Adding both we get the composition of final mixture as 11:39

which contains 22% raisins

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

22 Aug 2020, 23:44

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(X2-Avg)/(Avg-X1)=R1/R2

X2=30%
X1=20%
Avg=22%

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

1st Mix is 4 parts and 2nd Mix is just 1 part. Therefore, If 2nd mix is constant that 1st mix has to be 10*4= 40 pounds. We already have 5 pounds. Hence, we need 35 More.

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

20 Oct 2020, 16:33

We know the first snack mix is 20% raisins; the second snack mix is 30% raisins. How do week make a final blend of 22% raisins?

30 - 22 / 22 - 20 = 8/2 = 4/1

To get a mix of 22% we need 4 pounds of the first mix for every pound of the second mix.

We're told the first mix consists of 5 pounds and the second mix consists of 10 pounds. Therefore, we need an additional 35 pounds of the first mix.

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

18 Nov 2021, 01:35

2nd mix amount stays at 10 lbs

To get 22% final mix,

Where mix A = 20%

And

Mix B = 30%

We need to have Mix A be:

(30 - 22) / (30 - 20) = 8/10 of the entire mix

Right now

A = 5

B = 10

Use the answer choices until: (A) / (A + B) = 8/10 or 80%

(a) 25

(5 + 25) / (15 + 25) = 30 / 40 —- 75%

(b) 30

(5 + 30) / (15 + 30) = 35 / 45 = 7/9 = 77.77%

(C) 35

(5 + 35) / (15 + 35) = 40 / 50 = 80 / 100

80% is from mix A (40 lbs) and 20% is from Mix B (10 lbs)

Give us our 22% weighted average

C is the right answer: 40 - (5 already used) =

35

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

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Re: A snack mix that is 20% raisins is blended with a second mix that is 3 [#permalink]

19 Mar 2024, 03:09

GMAT Problem Solving (PS) Questions

A snack mix that is 20% raisins is blended with a second mix that is 3