SOLUTION: Why is it impossible to mix candy worth $4 per lb. and candy worth $5 per lb. to obtain a final mixture worth $6 per lb.?

Question 668245: Why is it impossible to mix candy worth $4 per lb. and candy worth $5 per lb. to obtain a final mixture worth $6 per lb.?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Why is it impossible to mix candy worth $4 per lb. and candy worth $5 per lb. to obtain a final mixture worth $6 per lb.?
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The value of the $4 candy plus the value of the $5 candy
can never equal the value of $6 candy
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4x + 5*(k-x) = 6*k has no solution:
4x + 5k-5x = 6k
-x = k
x = -k
But x is the amount of $4 candy; its weight cannot be -k
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Cheers,
Stan H.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If you got rid of the $4/lb candy and replaced it with more $5/lb
candy and kept adding more $5/lb candy, it would never be
worth more than $5/lb, and this is the best case you can have.
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