SOLUTION: The manager of a candy shop sells chocolate covered peanuts for $7 per pound and chocolate covered cashews for $12 per pound. The manager wants to mix 50 pounds of the cashews to g
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-> SOLUTION: The manager of a candy shop sells chocolate covered peanuts for $7 per pound and chocolate covered cashews for $12 per pound. The manager wants to mix 50 pounds of the cashews to g
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Question 1131466: The manager of a candy shop sells chocolate covered peanuts for $7 per pound and chocolate covered cashews for $12 per pound. The manager wants to mix 50 pounds of the cashews to get a cashew-peanut mixture that will sell for $8 per pound. How many pounds of chocolate covered peanuts should be used? Answer by greenestamps(13203) (Show Source):
Write and solve an equation that says the total value of the peanuts and cashews is equal to the total value of the mixture: x pounds of peanuts at $7 per pound, plus (50-x) pounds of cashews at $12 per pound, equals 50 pounds of mixture at $8 per pound.
That equation is relatively easy to solve using basic algebra. I leave it to you.
But here as a very different solution method that, if you understand it, can get you to answers to mixture problems like this faster and with less work.
I'll first show you all the calculations that are necessary, to see how easy they are; then I'll explain the method a bit.
12-8=4; 8-7=1; the ratio is 4:1.
50 pounds in a 4:1 ratio means 40 pounds of one and 10 pounds of the other.
Since the price for the mixture is closer to the price of the peanuts, the larger portion has to be peanuts.
ANSWER: 40 pounds of the peanuts and 10 pounds of the cashews.
The key to this solution method is that the ratio in which the two ingredients must be mixed is exactly determined by how far the price of the mixture is from the prices of the two ingredients. The $8 per pound price of the mixture is "4 times as close" to the $7 per pound cost of the peanuts as it is to the $12 per pound cost of the cashews; that means the mixture must contain 4 times as many peanuts as cashews.
