equations with three unknowns

Question

a coffee manufacturers has to blend 3 types of coffee beans to produce 10000 pounds. 3 component beans cost $2.4, $2.6, $2.00 per pound respectively. he wants to blend 10000 at total of 21000 dollars in blending the coffe there is one restriction that the amount used for component beans 1 and 2 are same. determine weather there is a combinatin of beans which will lead to a final blend of 10000 pounds costing $21000 and satisfying the restriction. Solve this word problem by making equations of three unknowns. i have tried so many tie but nota succeeding in finding solution.

Answer 1

 

b1 = $2.4/lb

b2 = $2.6/lb

b3 = $2.0/lb

 

Since the problem says b1 & b2 will be in equal amounts, we can create a 50-50 blend 'x' and set its price to $2.5/lb ( = (b1+b2)/2)

 

If 'n' represents the number of pounds of blend 'x' and 'm' represents the number of pounds of b3:

 

    2.5n + 2.0m =  21000    (1)

 

But also, the weights of the blend plus b3 must be 10000:

 

        n  +  m  = 10000    (2)

 

Solve:

   2n + 2m = 20000    (2 x eq (2))

   0.5n  = 1000           ( eq(1) - 2x eq(2))

 

       n = 2000

       m = 8000

 

This means  1000 lbs of b1, 1000 lbs of b2, and 8000lbs of b3 should do it.

 

Check:

 

  1000*2.4 + 1000*2.6 + 8000*2.0 = 21000 (ok)

and  1000+1000+8000 = 10000 (also ok)