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26 Nov 2014, 07:45
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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 Kudos for a correct solution. Source: Chili Hot GMAT [Reveal] Spoiler: OA _________________ Manager Joined: 12 Aug 2014 Posts: 150 Location: United States (AZ) Concentration: Finance, Strategy GMAT 1: 700 Q47 V39 Re: A wholesaler wishes to sell 100 pounds of mixed nuts at$2.50 a pound. [#permalink]

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26 Nov 2014, 08:40
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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)

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26 Nov 2014, 21:15
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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

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26 Nov 2014, 23:32
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] ### Show Tags 18 Nov 2016, 23:42 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] ### Show Tags 04 Jan 2018, 17:02 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 = $$\frac{100}{2.5}=\frac{1000}{25}= 40$$

*We know that (P + C) = 100. I wrote it that way to parallel the equation.
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