SOLUTION: A grocer mixes peanuts that cost $1.49 per pund and walnuts that cost $2.69 per pound to make 100 pounds of a mixture that costs $2.21 per pound. How much of each kind of nut did t

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Question 989797: A grocer mixes peanuts that cost $1.49 per pund and walnuts that cost $2.69 per pound to make 100 pounds of a mixture that costs $2.21 per pound. How much of each kind of nut did the grocer put into the mixture.
Answer by Edwin McCravy(20077) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of pounds of peanuts be x
Let the number of pounds of walnuts be y

                      Value      Value
Type       Number       of         of
 of          of          1        ALL
nuts       pounds     pound     poundss
-------------------------------------------
peanuts      x        $1.49     $1.49x
walnuts      y        $2.69     $2.69y
-------------------------------------------
mixture     100       $2.21   $221.00

 The first equation comes from the second column.

  %28matrix%285%2C1%2CNumber%2Cof%2Cpounds%2Cof%2Cpeanuts%29%29%22%22%2B%22%22%28matrix%285%2C1%2CNumber%2Cof%2Cpounds%2C+of%2Cwalnuts%29%29%22%22=%22%22%28matrix%285%2C1%2CNumber%2Cof%2Cpounds%2C+of%2Cmixture%29%29
                 x + y = 100

 The first equation comes from the last column.

  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cpeanuts%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cwalnuts%29%29%22%22=%22%22%28matrix%283%2C1%2CValue%2Cof%2Cmixture%29%29

           1.49x + 2.69y = 221

Get rid of decimals by multiplying every term by 100:

            149x + 269y = 22100

 So we have the system of equations:
           system%28x+%2B+y+=+100%2C149x+%2B+269y+=+22100%29.

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

           x + y = 100
               y = 100 - x

Substitute (100 - x) for y in 149x + 260y = 22100

    149x + 269(100 - x) = 22100
    149x + 26900 - 269x = 22100
          -120x + 26900 = 22100
                  -120x = -4800
                      x = 40 = the number of pounds of peanuts.

Substitute in y = 100 - x
              y = 100 - (40)
              y = 60 = the number of pounds of walnuts.

Checking:  40 peanuts is worth $59.60 and 60 pounds of walnuts is worth 
           $161.40
           That's 100 pounds that is worth = $221
           And 100 pounds of misture at 2.21 per pound is worth $221
           So it checks.

Edwin