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Difficulty:
35%
(medium)
Question Stats:
79% (02:13) correct
21%
(02:45)
wrong
based on 1439
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The cost of a mixture that contains candy-coated chocolate pieces and salted peanuts in the ratio of 2 pounds of chocolate pieces to 3 pounds of peanuts is $3.80 per pound. If the chocolate pieces cost $2.00 more per pound than the peanuts, how much do the peanuts cost per pound?
A. $0.90
B. $1.80
C. $2.28
D. $2.60
E. $3.00
A. $0.90
B. $1.80
C. $2.28
D. $2.60
E. $3.00
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Posts: 1
Cost for 5 pounds: 3.8*5=19
Cost of chocolate: C =P+2
Equation: 2(P+2) + 3P = 3.8*5=19
--> 5P = 15 --> P = 3
Cost of chocolate: C =P+2
Equation: 2(P+2) + 3P = 3.8*5=19
--> 5P = 15 --> P = 3
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houston1980
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
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General Discussion
gmatophobia
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houston1980
We can use teeter tooter method (or weighted averages) to solve this question.
Attachment:
Screenshot 2023-06-30 115935.jpg [ 24.21 KiB | Viewed 50547 times ]
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
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Posts: 32
houston1980
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
houston1980
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sayan640
Here you go sayan640
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
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 ?
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 ?
gmatophobia
Can this question be solved , using the alligation diagram ? Bunuel KarishmaB gmatphobia GMATinsight
https://gmatclub.com/forum/the-cost-of- ... l#p3221798
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houston1980
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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gmatophobia
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sayan640
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)
Quote:
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.
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
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
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:
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gmatophobia
thank you for the explanation. I have a doubt though. Why the ratio of weight (2:3) = ratio of prices ?
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2(x+2)+3x=3.8(2+3)
x=3
x=3
c:p = 2:3
C = 2T/5
P = 3T/5
T=total
((2T/5)Pc + (3T/5)Pp)/T = 3.8
2Pc/5 + 3Pp/5 = 3+ 4/5 = 19/5
2Pc + 3Pp = 19
Pc = Pp+2
2(Pp+2) + 3Pp = 19
2Pp + 4 = 3Pp = 19
5Pp = 15
Pp = 3
C = 2T/5
P = 3T/5
T=total
((2T/5)Pc + (3T/5)Pp)/T = 3.8
2Pc/5 + 3Pp/5 = 3+ 4/5 = 19/5
2Pc + 3Pp = 19
Pc = Pp+2
2(Pp+2) + 3Pp = 19
2Pp + 4 = 3Pp = 19
5Pp = 15
Pp = 3
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