SOLUTION: Fifteen pounds of trail mix are made by mixing 3 pounds of raisins worth $6 per pound with peanuts worth $3 per pound and chocolate coated candles worth $4 per pound how many pound

Question 1112071: Fifteen pounds of trail mix are made by mixing 3 pounds of raisins worth $6 per pound with peanuts worth $3 per pound and chocolate coated candles worth $4 per pound how many pounds of peanuts must be used if the mixture is to be worth $4.20 per pound
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Here is a non-traditional approach to the problem. Perhaps another tutor will see your question and my response and show you a more traditional method.

The mixture is to be 15 pounds worth $4.20 per pound, so the total value of the mixture is 15*$4.20 = $63.

The raisins are 3 pounds worth $6 per pound, so the value of the raisins is 3*$6 = $18. That means the other 12 pounds of peanuts and candies are worth $63-$18 = $45.

12 pounds worth $45 means $45/12 = $3.75 per pound.

Since $3.75 is "3 times as close" to $4 as it is to $3, there need to be 3 times as many candies at $4 per pound as there are peanuts at $3 per pound.

12 pounds of peanuts and candies, with three times as many pounds of candies as peanuts, means 9 pounds of candies and 3 pounds of peanuts.

ANSWER: 3 pounds of peanuts.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
Fifteen pounds of trail mix are made by mixing 3 pounds of raisins worth $6 per pound with peanuts worth $3 per pound
and chocolate coated candies worth $4 per pound how many pounds of peanuts must be used if the mixture is to be worth $4.20 per pound
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            ? ? ? Candles ? ? ?   Do you mean "candies" ? ? ?
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The way to solve this problem is to write AN EQUATION saying that the cost of ingredients is equal to the cost of the product.

Let x = the amount of peanuts to be used (in pounds), which is under the question. Since the amount of raisin is just given (3 pounds), then the amount of the candies must be (15-3-x) = (12-x) pounds. The cost of the ingredients is 6*3 dollars for 3 pounds of raisin 3*x dollars for x pounds of peanuts, and 4*(12-x) dollars for candiess. So the input costs 6*3 + 3x + 4*(12-x) dollars. The product must cost 4.20*15 dollars. So, "money" equation is 6*3 + 3x + 4*(12-x) = 4.20*15 Simplify and solve for x step by step 18 + 3x + 48 - 4x = 63 -x = 63 - 18 - 48 = -3 ====> x = 3. Answer. 3 pounds of peanuts must be mixed.

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P.S.   Although English is my second language, I am still able to make a distinguish between "candles" and "candies".

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