A waitress sold 12 steak dinners and 27 grilled salmon dinners, totaling $554.98 on a particular day. Another day she sold 26 ribeye steak dinners and 9 grilled salmon dinners, totaling &584.36. How much did each type of dinner cost?

the cost of rib eye steak dinner = $22.47

the cost of grilled salmon dinners = $10.57 ...

Step-by-step explanation:

Let x be the rib eye steak dinner.

Let y be the grilled salmon dinner.

According to the first given statement:

12x+27y = $554.98 (equation 1)

According to the second statement:

26x+9y=$584.36 (equation 2)

Lets take a look at the 1st equation:

12x+27y = $554.98

12x=$554.98 - 27y

x=$554.98 - 27y/12

Now substitute the value of x in 2nd equation:

26x+9y=$584.36

26 ($554.98 - 27y/12) + 9y=$584.36

26 (554.98 - 27y) + 9y=584.36*12

14429.48-702y=7012.32

-702y=7012.32-14429.48

-702y = - 7417.16

y = 7417.16/702

y=$10.57

Now substitute the value of y in equation 1:

12x+27y = $554.98

12x+27 (10.57) = 554.98

12x+285.39 = 554.98

Move the constant to the R. H. S

12x=554.98-285.39

12x=269.59

Divide both the terms by 12

12x/12=269.59/12

x=$22.47

Thus the cost of rib eye steak dinner = $22.47

the cost of grilled salmon dinners = $10.57 ...