A waitress sold 12 ribeye steak dinners and 39 grilled salmon totaling $575.53 on a particular day. Another day she sold 25 ribeye steak dinners and 13 grilled salmon dinners, totaling $582.43. How much did each type of dinner cost?

The cost of a ribeye steak dinner is $18.60.

The cost of a grilled salmon dinner is $9.03.

Step-by-step explanation:

let r be the cost of a ribeye steak dinner

let g be the cost of a grilled salmon dinner

Represent the two situations using equations:

12r + 39g = 575.53 (equation 1)

25r + 13g = 582.43 (equation 2)

The best method to use for this case is elimination, which is when you get rid of one of the variables by subtracting or adding.

Since the coefficients for "g" are 39 and 13, they can be eliminated if equation 2 was triple itself.

(25r + 13g = 582.43) X 3

= 75r + 39g = 1747.29 (new equation 2)

Subtract "equation 1" from "new equation 2"

. 75r + 39g = 1747.29

- 12r + 39g = 575.53

. 63r + 0g = 1171.76 <=we only deal with "r" because 0g is nothing

. 63r = 1171.76 <=divide both sides by 63 to isolate r

. r = 18.60 <=rounded from 18.599 ...

The cost of a ribeye steak dinner is $18.60.

Use any one of the equations to solve for "g", the cost of grilled salmon dinners. I will use equation 1.

12r + 39g = 575.53

Substitute r = 18.6

12 (18.6) + 39g = 575.53 <=only one variable now

223.2 + 39g = 575.53 <=subtract 223.2 from both sides

39g = 352.33 <=divide both sides by 39 to isolate g

g = 9.03 <=rounded from 9.0341 ...

The cost of a grilled salmon dinner is $9.03.