SOLUTION: A merchant has 5 pounds of mixed nuts that cost $30.He wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that co

Question 342037: A merchant has 5 pounds of mixed nuts that cost $30.He wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. How many pounds of peanuts are needed?
Found 2 solutions by checkley77, jrb1965:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Problem has no solution as stated BECAUSE:
You start with 5*30=$150 worth of mixed nuts.
To which you want to ADD peanuts @ $1.50 & cashews @ $4.50 per pound.
However you want to end up with 50 pounds costing $2.90 per pound.
50*2.90=$145.00 which is less than what you started with.

Answer by jrb1965(16) (Show Source): You can put this solution on YOUR website!
The 5 pounds of mixed nuts cost $30, not $30/LB. So the total mixture of 50# needs to cost 50LB * $2.90/LB = $145. The 5LB of mixed nuts cost $30, so the remaining 45LB need to cost $115. Peanuts + Cashews = 45LB, or P + C = 45. $1.50P + $4.50C = $115. Standard two equations in two unknowns. Solve the first equation for C, C= 45 - P, and substitute into the second equation, so
$1.50P + $4.50(45 - P) = $115
$1.50P + $202.50 - $4.50P = $115
$202.50 - $3.00P = $115
$3.00P = $87.50
P = 29.16667 LB
C = 45 - 29.16667 = 15.83333
Checking - 29.16667($1.50) + 15.83333($4.50) = $115
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