SOLUTION: A woman bought some large frames for$11 each and some small frames for $7 each at a closeout sale. If she bought 26 frames for $218, find how many of each type she bought.

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Question 1031571: A woman bought some large frames for$11 each and some small frames for $7 each at a closeout sale. If she bought 26 frames for $218, find how many of each type she bought.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of large frames be x
Let the number of small frames be y

                       Cost      Cost
Type       Number       of        of
 of          of        EACH       ALL
frame      frames     frame     frames
-------------------------------------------
large         x        $11       $11x
small         y         $7        $7y
-------------------------------------------
TOTALS       26      -----       $218

 The first equation comes from the "number of frames" column.

  %28matrix%284%2C1%2CNumber%2Cof%2Clarge%2Cframes%29%29%22%22%2B%22%22%28matrix%284%2C1%2CNumber%2Cof%2Csmall%2Cframes%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Cframes%29%29

                 x + y = 26

 The second equation comes from the last column.
  %28matrix%285%2C1%2CCost%2Cof%2CALL%2Clarge%2Cframes%29%29%22%22%2B%22%22%28matrix%285%2C1%2CCost%2Cof%2CALL%2Csmall%2Cframes%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Ccost%2Cof%2CALL%2Cframes%29%29

             11x + 7y = 218

 So we have the system of equations:

           system%28x+%2B+y+=+26%2C11x+%2B+7y+=+218%29.

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

           x + y = 26
               y = 26 - x

Substitute (26 - x) for y in 11x + 7y = 218

  11x + 7(26 - x) = 218
   11x + 182 - 7x = 218
         4x + 182 = 218
               4x = 36
                x = 9 = the number of large frames.

Substitute in y = 26 - x
              y = 26 - (9)
              y = 17 small frames.

Checking:  9 large frames cost $99 and 17 small frames is $119
            That's 26 frames.
            And indeed $99 + $119 = $218

Edwin