Question 1031571
<pre>
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.

  {{{(matrix(4,1,Number,of,large,frames))}}}{{{""+""}}}{{{(matrix(4,1,Number,of,small,frames))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,frames))}}}

                 x + y = 26

 The second equation comes from the last column.
  {{{(matrix(5,1,Cost,of,ALL,large,frames))}}}{{{""+""}}}{{{(matrix(5,1,Cost,of,ALL,small,frames))}}}{{{""=""}}}{{{(matrix(5,1,Total,cost,of,ALL,frames))}}}

             11x + 7y = 218

 So we have the system of equations:

           {{{system(x + y = 26,11x + 7y = 218)}}}.

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</pre>