A waitress sold 15 ribeye steak dinners and 14 grilled salmon dinners, totaling $583.59583.59 on a particular day. another day she sold 23 ribeye steak dinners and 7 grilled salmon dinners, totaling $580.74. how much did each type of dinner cost?

Step-by-step explanation:

This is a systems of equations question. Let's set ribeye steak to the variable r, and grilled salmon to s.

We get these two equations:

13r + 18s = 550.25

22r + 6s = 582.08

First, we'll isolate one variable in the first equation. Let's choose r:

13r = 550.25 - 18s

r = 42.33 - 1.38s

Now, we'll take this value for r and plug it into the second equation:

22r + 6s = 582.08

22 (42.33 - 1.38s) + 6s = 582.08

(931.19 - 30.46s) + 6s = 582.08 | multiply values by 22

931.19 - 24.46s = 582.08 | combine s values

349.11 = 24.46s | move 582.08 to left side, and combine; move - 24.46s to right side

14.27 = s | solve for s

Now, plug this value for s back into the first equation:

13r + 18s = 550.25

13r + 18 (14.27) = 550.25

13r = 256.91 = 550.25

13r = 293.34

r = 22.56

So r = 22.56 and s = 14.27.

The ribeye steak dinners cost $22.56 each and the grilled salmon dinners cost $14.27 each.

Note, this solution does not factor in any tips the waitress makes on each dinner!