SOLUTION: To mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound, how much of each kind of nut should be included in

Algebra ->  Expressions-with-variables -> SOLUTION: To mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound, how much of each kind of nut should be included in      Log On


   

Question 1154951: To mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound, how much of each kind of nut should be included in the mixed bag?
This is my answer: cashews: 0.42 lb.; peanuts: 0.08 1b.
Is this correct? Thank you.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x pounds of low priced
y pounds of high price
x at 2.3 dollar per pound
y at 5.5 dollar per pound

system%28x%2By=1%2F2%2C2.3x%2B5.5y=2.8%2A%281%2F2%29%29
-
x=1%2F2-y
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4.6x%2B11y=2.8
4.6%281%2F2-y%29%2B11y=2.8
2.3-4.6y%2B11y=2.8
6.4y%2B2.3=2.8
6.4y=0.5
y=0.078pounds the cashews, to two significant figures


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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Without doing any detailed calculations, no -- your answer is not right.

Your answer uses far more cashews than peanuts, so the price per pound should be much closer to $5.50 than it is to $2.30. But $2.80 is much closer to $2.30 than it is to $5.50.

A standard algebraic solution would go something like this....

x = pounds of cashews at $5.50 per pound
0.5-x = pounds of peanuts at $2.30 per pound

The combined mixture is a half pound worth $2.80 per pound:

x%285.5%29%2B%280.5-x%29%282.3%29+=+0.5%282.8%29

You can finish solving the problem by that method if you want. It is straightforward; but somewhat ugly, given all the decimals.

Here is a solution using the method I like to use for solving mixture problems like this.

(1) The target price per pound, $2.80, is 5/32 of the way from $2.30 to $5.50. (Picture the three prices -- 2.30, 2.80, and 5.50 -- on a number line. From 2.30 to 5.50 is 3.20; from 2.30 to 2.80 is 0.50. 2.80 is 0.50/3.20 = 5/32 of the way from 2.30 to 5.50.)

That means 5/32 of the mixture is the more expensive cashews.

ANSWER: (5/32) of the 1/2 pound mixture -- so 5/64 pounds -- are cashews; the remaining 27/64 pounds are peanuts.

CHECK:
%285%2F64%29%285.50%29%2B%2827%2F64%29%282.30%29+=+1.40
%281%2F2%29%282.80%29+=+1.40