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.

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) (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.

  

                 x + y = 26

 The second equation comes from the last column.
  

             11x + 7y = 218

 So we have the system of equations:

           .

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

RELATED QUESTIONS
a woman bought some large frames for $14 each and some small frames for $7 each at a... (answered by josmiceli)

A woman bought some large frames for $13 each and some small frames for $7... (answered by josmiceli)

(Can someone please help me with this question?) A woman bought some large frames for... (answered by ankor@dixie-net.com)

A woman bought some large frames for $17 each and some small frames for $7... (answered by addingup)

A woman bought some large frames for $17 each and some small frames for $8... (answered by Boreal)

A woman bought some large frames for $17 each and some small frames for $4... (answered by ikleyn)

Kim bought some large frames for $13 each and some small frames for $9 each at a closeout (answered by solver91311)

Karen Karlin bought some large frames for $15 each and some small frames for $8 each at a (answered by Fombitz)

A woman bought some large frames for $16each and some small frames for $4ech at close out (answered by ikleyn)