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Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai

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Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post Updated on: 11 Aug 2015, 11:32
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Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?

A) 16.67%
B) 23.33%
C) 25%
D) 33.33%
E) 36.67%

Originally posted by HarveyS on 08 Apr 2014, 16:08.
Last edited by ENGRTOMBA2018 on 11 Aug 2015, 11:32, edited 1 time in total.
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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 08 Apr 2014, 22:56
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Mountain14 wrote:
Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?

16.67%
23.33%
25%
33.33%
36.67%


Use scale method. First thing to do is to find out the ratio in which the two mixes were mixed together.

Sue's mix had 30% nuts and Jane's had 60%. Overall, it had 50% nuts

WSue/WJane = (60 - 50)/(50 - 30) = 1/2

So if Sue's mix was 100 gms (30 gm nuts, 70 gms dried fruit), it was mixed with 200 gms of Jane's mix.
So out of 300 gms of total mix, there was 70 gms of dried fruit i.e. (70/300) * 100 = 23.33%

Answer (B)
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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 08 Apr 2014, 20:09
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Let Sue's mix = a

Nuts \(= \frac{30a}{100}\)

Dry fruit \(= \frac{70a}{100}\)

Let Janes mix = b

Nuts \(= \frac{60b}{100}\)

Chocolate \(= \frac{40b}{100}\)

Combined mixture of Sue and Jane's trails mix contains 50% nuts

\(\frac{30a}{100} + \frac{60b}{100} = \frac{50}{100} (a+b)\)

3a + 6b = 5a + 5b

2a = b

It means quantity of Jane is twice that of Susan. Lets take numbers to solve this further

If Sue's mix = 10 gms, then Jane's mix = 20 Gms

Total = 10+20 = 30 Gms

Quantity of Dry fruits = 70% = 7 Gms

Percentage \(= \frac{7}{30} * 100 = 23.33%\)

Answer = B
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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 08 Apr 2014, 21:55
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Mountain14 wrote:
Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?

16.67%
23.33%
25%
33.33%
36.67%


Sol: Given that new mixture is 50 % nuts which is (50-30 =20) away from Sue's trail and (60-50=10) away from Jane's trail
Therefore, the ratio of Sue and Jane's mixture will be 1:2.

So if Sue's mixture is 100 gms then Jane's mixture will be 200 gms

From the table we can see that DF is 70 gm of Sue's mixture which is nothing 70/300*100 = 23.33%

Ans is A

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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 08 Apr 2014, 21:57
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Mountain14 wrote:
Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?

16.67%
23.33%
25%
33.33%
36.67%


Using alligation:

30 %.................60 %

...............50 %

10......................20

1 : 2

Hence both the mixtures are mixed in 1 : 2.

Let us say 10 grams of Suel's and 20 grams of Jane

Dried Fruit = 7

Total = 30

Percentage= 7/30 = 23.33 %

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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 19 Apr 2014, 03:15
1
Another Approach:

Whenever one part of the mixture is changed by mixing track that part. This is indirect approach which leads to same solution as through alligation.

Take X from 1 mixture
Take Y from 2 mixture

{0.3X + 0.6Y}/(X+Y) = 1/2

X:Y = 1:2

30+70+120+80=300

70/300
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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 28 Oct 2015, 14:39
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.3S+.6J=.5(S+J)
S/J=1/2
S/(S+J)=1/3
(1/3)(.7)=.2333=23.33%
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Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 02 Nov 2016, 08:59
I am using the following approach which I saw in similar problems but it seems that in no way it helps! Could anyone please tell what is wrong in the approach? Maybe I am committing a silly mistake.

N - F - Ch
30 70 0
60 0 40

Combining:

N F Ch
1800 4200 0
1800 0 1200
-----------------------
1800 4200 1200

Simplifying:

N F Ch
3 7 2

Asuming 100 g of total mixture:
12*x= 100 --> x= 100/12

Total g of F --> (100/12) * 7

The question ask for (F/total mixture). Hence:

(100/12)*7 / 100 = 7/12= 0.583 --> in percentage = 58.3%


Could you please tell? Thanks!
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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 19 Jul 2017, 16:51
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The first thing you should notice is that the combined mixture is 50% and Sue is at 30%. We can quickly see what would happen if the mixture was 1/1. It would be 0.3 + 0.6 then divided by 2 or 45%.

In order to get to 50% we must have more of Jane's mixture then Sue. With this in mind, it will make it easier to solve. We are going to figure out the proportion of S mixture to J= jane mixture. In my chart I used N1=Sue mixture amount and N2= Jane
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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 07 Dec 2017, 07:36
HarveyS wrote:
Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?

A) 16.67%
B) 23.33%
C) 25%
D) 33.33%
E) 36.67%


To start we can define a few variables:

x = the total amount of Sue’s trail mix, and y = the total amount of Jane’s trail mix

We are given that Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. We can represent this below:

Nuts in Sue’s trail mix = 0.3x

Dried fruit in Sue’s trail mix = 0.7x

Nuts in Jane’s trail mix = 0.6y

Chocolate chips in Jane’s trail mix = 0.4y

We are also given that when the two trail mixes are combined, the resulting trail mix will contain 50% nuts. Since nuts in Sue’s trail mix = 0.3x, nuts in Jane’s trail mix = 0.6y, and the total weight of the two trail mixes is x + y, we can create the following equation:

(0.3x + 0.6y)/(x + y) = 50% = 0.5

0.3x + 0.6y = 0.5x + 0.5y

0.1y = 0.2x

y = 2x

Now we can determine what percent of the combined mixture is dried fruit. Since only Sue’s mixture contains dried fruit, we know that the only dried fruit in the mixture is 0.7x. We also know that the total weight of the mixture is x + y, so we can create the following ratio:

0.7x/(x + y)

0.7x/(x + 2x)

0.7x / 3x

0.7/3 = 0.2333…

So, the combined trail mix contains approximately 23.33% dried fruit.

Answer: B
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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 14 Mar 2018, 19:57
Hi All,

This question can be solved with a bit of algebra:

Sue's Mix: 30% nuts and 70% dried fruit
Jane's Mix: 60% nuts and 40% chocolate

Combined mix is 50% nuts…so we can create the follow equation:

X = number of servings of Sue's Mix
Y = number of servings of Jane's Mix

(.3X + .6Y)/(X + Y) = .5

.3X + .6Y = .5X + .5Y

.1Y = .2X

Y = 2X

This means that the mixture is "1 part" Sue's Mix and "2 parts" Jane's Mix, with a Total of 3 parts.

The question asks what percent of the Total Mix is dried fruit….

1(.7)/(1+2) = .7/3

Since .75/3 = 25%…

.7/3 has to be a little less than 25%

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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 30 Dec 2018, 22:11
Bunuel Can you please link to similar questions? Thank you so much!
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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 22 Jan 2019, 17:21
HarveyS wrote:
Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?

A) 16.67%
B) 23.33%
C) 25%
D) 33.33%
E) 36.67%


IMO the best way to solve this question is to use allegation.

ratio of Sue : Jane's trail mix must be in a 1:2 ratio.

That means total will be 100% Sue and 200% Jane, total mixture is 300% original size.

Sue's mixture has 70% dried fruit so \(\frac{70}{300} = 23.33%\)
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Re: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 29 May 2019, 09:38
Let Sue's mixture be x, and Jane's mixture be y.
Nuts %age => 0.3x+0.6y/(x+y) * 100 = 50
This simplifies into y=2x
Dry fruits %age => 0.7x/x+y * 100
=> 0.7x/3x * 100 = 23.33

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Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai  [#permalink]

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New post 09 Aug 2019, 21:37
See image for Step 1.
Note: we assumed a total weight of 100 units for step 1.

Step 2 - Determine the amount that Sue's mix contributes to final mix i.e. determine x

0.3x +0.6(100-x)= 50
0.3x+60-0.6x=50
-0.3x=-10
3x/10=10
3x=100
x=100/3 (this is the weight of Sue's mix)

Step 3 - determine the amount of fruit
Since we know the weight of Sue's mix, we can use the proportion given to us.
Fruit = 70%

7/10 * 100/3
=70/3
=23 1/3
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Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai   [#permalink] 09 Aug 2019, 21:37
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