Answer:
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!
