SOLUTION: Peanuts are worth $2 per pound and cashews are worth $12 per pound. How many pounds of each must you mix to get 20 pounds of mixed nuts that are worth $5 per pound? I think I have

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Question 86284: Peanuts are worth $2 per pound and cashews are worth $12 per pound. How many pounds of each must you mix to get 20 pounds of mixed nuts that are worth $5 per pound? I think I have the equation and what part of the equation is for each part.
5(x+y)=2x+12y

x=lbs of nuts
y=lbs of cashews
x+y=final mixture
2x=value of peanuts
12y=value of cashews
$5=mixture per lb
If you can help, I would greatly appreciate it.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Peanuts are worth $2 per pound and cashews are worth $12 per pound. How many pounds of each must you mix to get 20 pounds of mixed nuts that are worth $5 per pound? I think I have the equation and what part of the equation is for each part.
5(x+y)=2x+12y
:
x=lbs of nuts
y=lbs of cashews
x+y=final mixture
2x=value of peanuts
12y=value of cashews
$5=mixture per lb
:
Using your information:
:
Actually the final mixture would be 5(20), so you have:
2x + 12y = 5(20)
2x + 12y = 100
:
Also we know:
x + y = 20
x = (20 - y)
:
Substitute (20-y) for x, find y:
2(20-y) + 12y = 100
40 - 2y + 12y = 100
-2y + 12y = 100 - 40
10y = 60
y = 6 lb of cashews
:
x = 20 - 6 = 14 lb of peanuts:
:
:
Check solution:
2(14) + 12(6) =
28 + 72 = 100