SOLUTION: A merchant wishes to blend 200 pounds of coffee to be worth $3.20 per pound from two types of coffee; one is worth $3.00 per pound and the other is worth $3.25 per pound. How many

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A merchant wishes to blend 200 pounds of coffee to be worth $3.20 per pound from two types of coffee; one is worth $3.00 per pound and the other is worth $3.25 per pound. How many       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1030299: A merchant wishes to blend 200 pounds of coffee to be worth $3.20 per pound from two types of coffee; one is worth $3.00 per pound and the other is worth $3.25 per pound. How many pounds of each mixture should he use?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of pounds of cheaper coffee be x
Let the number of pounds of costlier coffee be y


                       Value      Value
 Type       Number      of         of
 of          of        EACH        ALL
coffee     pounds     pound      pounds
-------------------------------------------
cheaper      x      $3.00       $3.00x
costlier     y      $3.25       $3.25y
-------------------------------------------------
mixture     200     $3.20   200($3.20) = $640.00

 The first equation comes from the "Number of pounds" column.

  %28matrix%286%2C1%2CNumber%2Cof%2Cpounds%2C+of%2Ccheaper%2Ccoffee%29%29%22%22%2B%22%22%28matrix%286%2C1%2CNumber%2Cof%2Cpounds%2Cof%2Ccostlier%2Ccoffee%29%29%22%22=%22%22%28matrix%287%2C1%2Ctotal%2Cnumber%2Cof%2Cpounds%2Cof%2Cmixture%2Ccoffee%29%29

                 x + y = 200

 The second equation comes from the last column.
  %28matrix%285%2C1%2CValue%2Cof%2CALL%2Ccheaper%2Ccoffee+%29%29%22%22%2B%22%22%28matrix%285%2C1%2CValue%2Cof%2CALL%2Ccostlier%2Ccoffee%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoffee%29%29

           3.00x + 3.25y = 640.00

Get rid of decimals by multiplying every term by 100:

             300x + 325y = 64000

 So we have the system of equations:
           system%28x+%2B+y+=+200%2C300x+%2B+325y+=+64000%29.

We solve by substitution.  Solve the first equation for y:

           x + y = 200
               y = 200 - x

Substitute (200 - x) for y in 300x + 325y = 64000

    300x + 325(200 - x) = 64000
    300x + 65000 - 325x = 64000
           -25x + 65000 = 64000
                   -25x = -1000
                      x = 40 = the number of pounds of cheaper.

Substitute in y = 200 - x
              y = 200 - (40)
              y = 160 pounds of costlier.

Checking:  40 pounds of cheaper is $120.00 and 160 
           pounds of costlier is $520.00
           That's 200 pounds of mixed coffee.
           And indeed $120.00 + $520.00 = $640.00

Edwin