The cost of a mixture that contains candy-coated chocolate pieces

We can use teeter tooter method (or weighted averages) to solve this question.


On a number line, the price of chocolates lies two units right to the price of the salted peanuts.

The distance of 2 between the chocolates and peanuts is divided into a ratio of 2:3.

\(\frac{2}{5} = 0.4\)

Price of peanuts = $ 3.80 - 2 * (0.4) = 3.8 - 0.8 = $3

Option E

Let x be the peanuts’ cost per pound.

Since the dollar-per-pound cost of the mixture is the weighted arithmetic average of the dollar-per-pound costs of its components, we have:

[2(x + 2) + 3x]/5 = 3.8

5x + 4 = 19

x = 3

Therefore, the peanuts cost $3 per pound.

Answer: E

the tricky part here is the mixture cost is given per pound ie 3.80 but the quantities given total up to 5 pounds
2c+3p = 3.80*5
c=2+p
2(2+p)+3p =19
5p = 15
p=3
ans E
(c = chocolate coated candy , p= peanuts )

Can this question be solved , using the alligation diagram ? Bunuel KarishmaB gmatphobia GMATinsight
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gmatphobia , thank you for the wonderful explanation.
So the general rule of the alligation , is as follows ,
We need to keep the similar quantities in the upper side of the diagram. 
Here in this case , (x+2) , 3.80 and x are  the values  ( of chocolates/ peanuts)  or dollar amounts.
So we kept them all in the upper side of the diagram.
And then subtract from their mean i.e 3.80 to find out their corresponding weights in the mixture.
Here, (x-3.80) and (3.80 - (x+2))  are the corresponding weights  in the mixture  that we derive.
Correct me if I am wrong in explaining the alligation concept.gmatphobia
I have got a question for you , gmatphobia  / Bunuel / KarishmaB .
In  the diagram , why is it  that 3.80 is bigger than (x+2) ? ; gmatphobia wrote 3.80 - (x+2). Why ?
Or for that matter , how do you know that x is bigger than 3.80 ? You wrote  (x -3.80).
Please help. gmatphobia  KarishmaB Bunuel
gmatphobia/ KarishmaB , Can you please help ?
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Can this question be solved , using the alligation diagram ? Bunuel KarishmaB gmatphobia GMATinsight
gmatophobia 's method here uses the scale method and shows you the power of weighted averages.
https://gmatclub.com/forum/the-cost-of- ... l#p3221798
 
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There are a couple of fundamental things that are going behind the scenes (and that's why a formula-based approach is not recommended unless one knows the mechanics behind that formula) 
We need to realize that (x+2) > (x), and as the mixture contains more quantity of peanuts (why did I infer this ? Because the question states that "ratio of 2 pounds of chocolate pieces to 3 pounds of peanuts"), the value of the mixture will be closer to the value x. Therefore 3.80 is not greater than (x+2), but is less. 
The order of subtraction doesn't matter as long as you're keeping the ratios intact. 

For example, x : y = 2:1 is the same as y : x = 1:2. So the quantity we are expressing in numerator and denominator matters.

So whether we solve ⇒

\( \frac{\text{Peanuts}}{\text{Chocolate Pieces}} = \frac{(x+2) - 3.8}{3.8-x}\)­

\( \frac{3}{2} = \frac{(x+2) - 3.8}{3.8-x}\)­ ➾, In this case, the values of the numerator and denominator are positive

\((3 * 3.8) - 3x = 2x + 4 - (2*3.8)\)

\(x = 3.8 - 0.8 = 3\)

or we solve 

\( \frac{\text{Chocolate Pieces}}{\text{Peanuts}} = \frac{x - 3.8 }{3.8 - (x+2)}\)­

\( \frac{2}{3} = \frac{x - 3.8 }{3.8 - (x+2)}\)­ ➾, In this case, the values of the numerator and denominator are negative and they cancel out.

\((2 * 3.8) - 2x - 4 = 3x - (3.8 * 3)\)

\(x = 3.8 - 0.8 = 3\)

we would get the same value.

Hope this helps. ­

gmatophobia ,  you said that "We need to realize that (x+2) > (x), .." .
Reason why  (x+2) > (x) ?
 It is because the average value of (x+2) and x is 3.80. Hence one has to be larger and the other has to be smaller than 3.80. Hence , obviously ( x+2 ) is on the other side of the mean and is larger. Please correct  me  if I am wrong . gmatphobia Bunuel
Also you said that "....the value of the mixture will be closer to the value x. .." 
Reason why "the value of the mixture will be closer to the value x" ?
Since  'x' is the value of peanuts whose weight/ quantity is larger  in the mixture , the value of the mixture will be closer to the value x . Correct me if my reasoning is  wrong. gmatphobia
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­Turn your decimals into fractions:

­thank you for the explanation. I have a doubt though. Why the ratio of weight (2:3) = ratio of prices ?

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Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com

2(x+2)+3x=3.8(2+3)
x=3