SOLUTION: a metal worker has a 30% copper and another alloy that is 60% copper. how many killograms of each alloy should the metal worker combine to create 80 kg of a 48% copper alloy

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Question 1007274: a metal worker has a 30% copper and another alloy that is 60% copper. how many killograms of each alloy should the metal worker combine to create 80 kg of a 48% copper alloy
Found 2 solutions by Edwin McCravy, lwsshak3:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of kgs. of Alloy1 be x
Let the number of kgs. of Alloy2 be y


                                 Number
Type       Number   Percent      of kg
 of        of kg    which is    of copper
coin      of metal   copper     in each
-------------------------------------------
Alloy1       x       0.30        0.30x
Alloy2       y       0.60        0.60y
-------------------------------------------
mixture     80      0.48        0.48(80)

 The first equation comes from the second column.

  %28matrix%283%2C1%2CKilograms%2Cof%2CAlloy1%29%29%22%22%2B%22%22%28matrix%283%2C1%2Ckilograms%2Cof%2CAlloy2%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Ckilograms%2Cof%2Calloy%29%29

                 x + y = 80

 The second equation comes from the last column.
  %28matrix%286%2C1%2CKilograms%2Cof%2CPURE%2CCOPPER%2Cin%2CAlloy1%29%29%22%22%2B%22%22%28matrix%286%2C1%2CKilograms%2Cof%2CPURE%2CCOPPER%2Cin%2CAlloy2%29%29%22%22=%22%22%28matrix%286%2C1%2CKilograms%2Cof%2CPURE%2CCOPPER%2Cin%2Cmixture%29%29

           0.3x + 0.6y = 0.48(80)

           0.3x + 0.6y = 38.4


Get rid of decimals by multiplying every term by 10:

               3x + 6y = 384

 So we have the system of equations:
           system%28x+%2B+y+=+80%2C3x+%2B+6y+=+384%29.

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

           x + y = 80
               y = 80 - x

Substitute (80 - x) for y in 30x + 60y = 3840

      3x + 6(80 - x) = 384
       3x + 480 - 6x = 384
           -3x + 480 = 384
                 -3x = -96
                   x = 32 = the number of kg. of Alloy1.

 Substitute in y = 80 - x
               y = 80 - 32 = 48 kg. of Alloy2. 
Edwin

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
a metal worker has a 30% copper and another alloy that is 60% copper. how many killograms of each alloy should the metal worker combine to create 80 kg of a 48% copper alloy
let x=amt of 30% alloy to use
80-x=amt of 60% alloy to use
30%x+60%(80-x)=48%*80
.30x+48-.60x=38.4
.30x=9.6
x=32
80-x=48
amt of 30% alloy to use=32 kg
amt of 60% alloy to use=48 kg