SOLUTION: A manager sell peanuts for $2.50 per pound. He wants to mix cashews that sell for $5.00 a pound with the peanuts to create 30 pounds of a mixture that sells for $4.00 a pound. How
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Question 98428: A manager sell peanuts for $2.50 per pound. He wants to mix cashews that sell for $5.00 a pound with the peanuts to create 30 pounds of a mixture that sells for $4.00 a pound. How many pounds of each nut are needed.
please show me how to set this up and solve it Found 2 solutions by checkley71, Earlsdon:Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website! 30*4=2.5x+5*(30-x)
120=2.5x+150-5x
120-150=2.5x-5x
-2.5x=-30
x=-30/2.5
12 pounds of $2.50 peanuts are needed.
30-12=18 pounds of $5.00 cashews are needed.
proof
30*4=2.5*12+5*18
120=30+90
120=120
You can put this solution on YOUR website! Well, you can start by assigning variables to the unknown quantities.
Let P = the number of pounds of peanuts at $2.50 per pound.
Let C = the number of pounds of cashews at $5.00 per pound.
From the problem description, you are told that P + C = 30 pounds and this mixture will cost $4.00 per pound.
We have enough information to set up the necessary equation, but there are two unknowns and only one equation. We need to reduce the number of unknowns to only one.
$2.50(P) + $5.00(C) = $4.00(30) but you are also told that:
P + C = 30 which can be written as C = 30 -P so we'll replace the C with 30-P.
$2.50(P) + $5.00(30-p) = $4.00(30) Now you can simplify this and solve for P.
2.5P+5(30-P) = 4(30)
2.5P+150-5P = 120 Combining like-terms, we get:
-2.5P = -30 Divide both sides by -2.5
P = 12 You will need 12 pounds of peanuts.
C = 30-P
C = 30-12
C = 18 You will need 18 pounds of cashews.
Check:
Cost of 12 pounds of peanuts + cost of 18 pounds of cashews = cost 0f 30 pounds of mixed nuts at $4.00 per pound.
$2.50(12) + $5.00(18) = $4.00(30)
$30.00 + $90.00 = $120
$120.00 = $120.00
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