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A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound.

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A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. [#permalink]

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Tough and Tricky questions: Mixture Problems.



A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?

A) 40
B) 45
C) 50
D) 55
E) 60

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Source: Chili Hot GMAT
[Reveal] Spoiler: OA

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Re: A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. [#permalink]

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New post 26 Nov 2014, 07:40
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From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y

From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:

$2.5 * (x + 100 - x) = $1.5x + $4(100 - x)

If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.

You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)

Answer is A.

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Re: A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. [#permalink]

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New post 26 Nov 2014, 10:43
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I used simultaneous equations. Let p = pounds of peanuts and c = pounds of cashews.
p+c=100
1.5p+4c=100*2.50=250

Multiply the first equation by (-4) and add the two equations: -2.5p=-150, thus we have 60 pounds of peanuts and 40 pounds of cashews.
Choice A

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Re: A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. [#permalink]

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New post 26 Nov 2014, 20:15
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Cashews /peanuts = (Mean price - peanuts price)/(Cashew price - Mean price) = (2.5-1.5)/(4-2.5) = 2/3
Cashew = (2/5)*100 = 40Kg

Answer is A.

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Re: A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. [#permalink]

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New post 26 Nov 2014, 22:27
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Answer = A) 40

Refer diagram below:

Attachment:
alliga.png
alliga.png [ 3.23 KiB | Viewed 2158 times ]


In 2.5 pound mixture, 1 pound cashews would be required

So in 100 pound, requirement of cashews \(= \frac{100}{2.5} = 40\)
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Re: A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. [#permalink]

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New post 26 Nov 2014, 22:32
Peanut ......................... Cashews ................... Total

100-x ................................ x .............................. 100 (Say "x" is the quantity of cashews in 100 pounds)

1.5 .................................. 4 ................................ 2.5 (Pricing/pound)

Setting up the equation

1.5(100-x) + 4x = 100*2.5

x = 40
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Re: A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. [#permalink]

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New post 18 Nov 2016, 22:42
Bunuel wrote:

Tough and Tricky questions: Mixture Problems.



A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?

A) 40
B) 45
C) 50
D) 55
E) 60

Kudos for a correct solution.

Source: Chili Hot GMAT


number of pounds = total selling price / price per pound or total cost / cost per pound , thus we use prices or cost as weights

w1/w2 = 3/2 thus w1 = 3x , w2 = 2x , hence 100 = 5x and thus x is 20 , the average price is 2.5 closer to that of peanuts (1.5) than it is to that of cashew then

cashew takes the smaller weight that is 2x thus cashew weight is 2(20) =40

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A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. [#permalink]

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New post 04 Jan 2018, 16:02
Bunuel wrote:

Tough and Tricky questions: Mixture Problems.



A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?

A) 40
B) 45
C) 50
D) 55
E) 60

Kudos for a correct solution.

Source: Chili Hot GMAT

A weighted average approach I use in mixture problems. Here, peanuts cost an "average" of $1.50 per pound. Cashews cost an average of $4.00 per pound.
\(Ave_{A}(Qty_{A}) + Ave_{B}(Qty_{B}) = Ave_{A+B}(Qty_{A+B})\)

Where \(Ave_{A+B}\) is the desired cost of the resultant mixture of nuts

Let P = # of pounds of peanuts at $1.50 a pound
Let C = # of pounds of cashews at $4.00 a pound
P + C = 100
P = 100 - C

1.50(P) + 4.00(C) = 2.50(P + C)*
1.5(100 - C) + 4(C) = 2.5(100)
150 - 1.5C + 4C = 250
2.5C = 100
C = \(\frac{100}{2.5}=\frac{1000}{25}= 40\)

Answer A

*We know that (P + C) = 100. I wrote it that way to parallel the equation.
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A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound.   [#permalink] 04 Jan 2018, 16:02
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