What is the optimal ratio of peanuts to cashews for maximum revenue?

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Homework Help Overview

The problem involves determining the optimal ratio of peanuts to cashews in a mixture to achieve maximum revenue. The context includes selling cashews at $5.00 per pound and peanuts at $1.50 per pound, with a mixture sold at $3.00 per pound.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the setup of the equations related to revenue from selling the nuts separately versus as a mixture. There is an attempt to clarify the correct interpretation of the problem regarding the quantities of peanuts and cashews.

Discussion Status

Some participants express confusion over the stated "correct answer" of 22.5 pounds of peanuts, questioning its relevance to the original question about the amount of cashews needed. This indicates a potential misunderstanding or miscommunication regarding the problem's requirements.

Contextual Notes

There is mention of the problem being part of a review on matrices, suggesting that the participants are navigating through concepts that may not be fully grasped yet. The reference to the back of the book as a source of the "correct answer" introduces an element of uncertainty regarding the accuracy of the provided solution.

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Homework Statement



A store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?


Homework Equations



x1 + y1 = k1
x2 + y2 = k2

The Attempt at a Solution



x= cashews
y= peanuts

5x + 1.5y = 3(x+y)

5(30) +1.5y = 3(30+y)

150 +1.5y = 90 + 3y

60 = 1.5y

40 = y

Correct answer: 22.5 pounds of peanuts


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I know this isn't probably pre-calculus, but my teacher is reviewing matrices, and this is the first section of the chapter. I usually don't have problems doing these types of problems, especially problems relating to the mixing of nuts/candies, etc. But, for some odd reason, I'm not getting the correct answer, and I think my set-up is probably wrong. I don't see another logical way to approach this question.

Any help is greatly appreciated!
 
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Your set up and answer seem right to me. Who says the answer is 22.5 lbs?
 
The back of the book, apparently.
 
How can the "correct answer" possibly be "22.5 lbs of peanuts" when the question is "how many pounds of cashews"?
 
Yikes! Hallsofivy is right!
 

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