Awaitress sold 10 ribeye steak dinners and 18 grilled salmon dinners, totaling $590.39 on a particular day. anither day she sold 22 ribeye steak dinners and 9 grilled salmon dinners, totaling $583.49. how much did each type of dinner cost? a) the cost of ribeye steak dinners is $__b) the cost of salmon dinners is $__

   a) The cost of ribeye steak dinners is $ 16.96.

   b) The cost of grilled salmon dinners is $ 23.37.

Explanation:

 Let the cost for ribeye steak dinners  be m and cost for grilled salmon dinners  be n.

 A waitress sold 10 ribeye steak dinners and 18 grilled salmon dinners, totaling $590.39 on a particular day.

So, we have    

         10 m + 18 n = 590.39 equation 1

Another day she sold 22 ribeye steak dinners and 9 grilled salmon dinners, totaling $583.49

So, we have    

         22 m + 9 n = 583.49 equation 2

 equation 2 x 2

       44 m + 18 n = 1166.98 equation 3

 equation 3 - equation 1

        44 m + 18 n - (  10 m + 18 n ) = 1166.98 - 590.39

         m = 16.96 $

  Substituting in equation 1

        22 x 16.96 + 9 n = 583.49

          n = 23.37 $

   a) The cost of ribeye steak dinners is $ 16.96.

   b) The cost of grilled salmon dinners is $ 23.37.

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