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

[Lurid]

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!

 

[Chestermiller]

Your set up and answer seem right to me. Who says the answer is 22.5 lbs?

 

[Lurid]

The back of the book, apparently.

 

[HallsofIvy]

How can the "correct answer" possibly be "22.5 lbs of peanuts" when the question is "how many pounds of cashews"?

 

[Chestermiller]

Yikes! Hallsofivy is right!