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have nuts that cost $9.00 per pound and 50 pounds of nuts that cost $5.00 per pound how many pounds do i need to get a mixture that cost $6.50 per pound

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2 Answers

 Here again choose a variable for the unknown, what problem is asking you to find out. 
 
     X - amount of $9.00/ lb need to be mixed with $5.00/ lb
 
     X ( 9.00) + 5( 50) = ( X + 50) (6.50)    to mixing means adding up the  weights .
       9X + 250 = X ( 6.50) + 325
     
     9X - 6.50 X = 325 - 250
     
       2.50 X = 75
 
        X = 75/ 2.50 = 30 lb 
You are given the amount of the cheaper nut: 50 lbs. 
You need to know the amount of the more expensive nut; let that be x.
The total weight of the final mixture is 50+x.
 
So we have x pounds times $9 plus 50 pounds times $5 equals $6.50 times the sum of x and 50.
 
9x + 5*50 = 6.5*(x+50)
9x + 250 = 6.5x + 325
9x = 6.5x +75
2.5x=75
x = 30
 
Adding 30 lbs of the more expensive nut will create 80 lbs of a mixture that costs $6.50 per pound.