SOLUTION: A man wants to blend 30kg of coffee and each kilo cost $4.80. One brand of coffee cost $6 dollars and $4 dollars for a kilo. How much kilos of each brand of coffee should be used

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Question 539307: A man wants to blend 30kg of coffee and each kilo cost $4.80.
One brand of coffee cost $6 dollars and $4 dollars for a kilo. How
much kilos of each brand of coffee should be used?
Found 2 solutions by josmiceli, AnlytcPhil:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = kg of $6/kg coffee needed
Let b = kg of $4/kg coffee needed
given:
+6a+ = cost of $6 coffee
+4b+ = cost of $4 coffee
----------------------
(1) +a+%2B+b+=+30+ kg
(2) +%28+6a+%2B+4b+%29%2F+30+=+4.8+ dollars
-------------------------
(2) +6a+%2B+4b+=+144+
(2) +3a+%2B+2b+=+72+
Multiply both sides of (1) by 2 and
subtract (1) from (2)
(2) +3a+%2B+2b+=+72+
(1) +-2a+-+2b+=+-60+
+a+=+12+
and, since
(1) +a+%2B+b+=+30+
(1) +b+=+18+
12 kg of $6/kg coffee are needed
18 kg of $4/kg coffee are needed
check:
(2) +%28+6a+%2B+4b+%29%2F+30+=+4.8+
(2) +%28+6%2A12+%2B+4%2A18+%29%2F+30+=+4.8+
(2) +%28+72+%2B+72+%29+%2F+30+=+4.8+
(2) +144+=+4.8%2A30+
(2) +144+=+144+
OK

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
A man wants to blend 30kg of coffee and each kilo cost $4.80.
One brand of coffee cost $6 dollars and $4 dollars for a kilo. How
much kilos of each brand of coffee should be used?
Suppose we mix x kg of the $6 coffee with y kg of the $4 coffee.
Then we have two equations, a coffee equation and a money equation:

The coffee equation comes from

         %28matrix%286%2C1%2Cx%2C+kgs%2C+of%2C+more%2C+expensive%2C+coffee%29%29 + %28matrix%286%2C1%2Cy%2C+kgs%2C+of%2C+less%2C+expensive%2Ccoffee%29%29 = %28matrix%287%2C1%2C30%2C+kgs%2C+of%2C+medium%2C+priced%2C+mixed%2C+coffee%29%29  


                          x + y = 30

The money equation comes from
    
          + %28matrix%288%2C1%2C%22%244%22%2C+times%2Cy%2C+kgs%2C+of%2C+less%2C+expensive%2Ccoffee%29%29 =   

                        $6x + $4y = ($4.80)(30)
                          6x + 4y = 144

So solve this system of equations:

                         x +  y =  30
                        6x + 4y = 144


Answer: Mix 12 kgs of the more expensive coffee and 18 kgs of the cheaper coffee

Edwin