SOLUTION: The owner of Nuts2U Snack Shack mixes cashews worth ​$6.25 a pound with peanuts worth ​$2.30 a pound to get a​ half-pound, mixed-nut bag worth ​

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Question 1100856:
The owner of Nuts2U Snack Shack mixes cashews worth ​$6.25

a pound with peanuts worth ​$2.30

a pound to get a​ half-pound, mixed-nut bag worth ​$1.90
.
How much of each kind of nut is included in the mixed​ bag?
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The owner of Nuts2U Snack Shack mixes cashews worth ​$6.25
a pound with peanuts worth ​$2.30 a pound to get a​ half-pound, mixed-nut bag worth ​$1.90
.
How much of each kind of nut is included in the mixed​ bag?
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Equations:
Value:: 6.25c + 2.30p = 1.90
Quantity:: c + p = 1/2
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Modify for elimination::
625c + 230p = 190
625c + 625p = 312.5
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Subtract and solve for "p"
395p = 122.5
p = 0.31 lbs (amt of peanuts to use)
c = 0.5-0.31 = 0.19 lbs (amt of cashews to use)
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Cheers,
Stan H.
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Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
This is just like any two-part mixture problem. So many have already been solved on the site.

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Make M pounds mix of y pounds of item worth H dollars per pound and x pounds of item worth L dollars per pound so that the mixture made is T dollars per pound.
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x%2By=M
y=M-x
-
Lx%2BH%28M-x%29=T%2AM-------equation in ONE unknown variable, x
Lx%2BHM-Hx=TM
Lx-Hx%2BHM=TM
%28L-H%29x=TM-HM
multiplybothsidesby-1;
%28H-L%29x=HM-TM
highlight%28x=%28HM-TM%29%2F%28H-L%29%29
and use the found value of x to evaluate y.

Substitute the given values for M, H, L, and T.

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Notice that the given exercise description starts with peanuts $2.30 per pound and cashews worth $6.25 per pound and asks for a mixture worth $1.90 per pound. This CANNOT happen. The mixture can NOT be a lower price than either of the two prices for the starting materials.