How to solve this problem using elimination method?

Question

Macadamia nuts cost $16.50 per pound. Regular nuts cost $9.25 per pound. How many pounds of macadamia nuts and how many pounds of regular nuts should I combine to produce 40 pounds of a mixed nut concoction that will cost $10 per pound?

Answer 1

x = Macadamia nuts 

y = regular nuts

 

Set up 2 equations

$16.50x + $9.25y = $400

          x  +        y =     40

 

Multiply 2nd equation by -9.25 and then add two equations to eliminate y variable 

 

16.50x  +  9.25y =  400

 -9.25x + -9.25y =  40  x  (-9.25) 

  7.25x    =   30

        x     =  4.14

 

Replace x with 4.14 and solve for y

 

16.50(4.14) 9.25y  =  400

68.31  +      9.25y  =  400

9.25y  =   331.69

      y  =  35.86

 

 

  4.14 lbs of macadamia nuts

35.86 lbs. of regular nuts

 

 

 

Macadamia Nuts    $16.50 x   4.14 lbs =  $  68.31

Regular Nuts             9.25 x 35.86 lbs =  $331.71

Total                                   40.00           $400.02

 

Cost/Pound ($400/40 lbs.)                       $10.00