To find the cost of each type of dinner (ribeye steak and grilled salmon), we can set up a system of equations based on the given information.
Let's assume the cost of a ribeye steak dinner is $x, and the cost of a grilled salmon dinner is $y.
From the first day's information:
1. 17 ribeye steak dinners and 18 grilled salmon dinners totaled $582.53.
This gives us the equation: 17x + 18y = 582.53.
From the second day's information:
1. 28 ribeye steak dinners and 6 grilled salmon dinners totaled $582.72.
This gives us the equation: 28x + 6y = 582.72.
Now, we have a system of two equations:
1) 17x + 18y = 582.53
2) 28x + 6y = 582.72
We can solve this system of equations to find the values of x and y.
First, let's eliminate one variable. We can do this by multiplying both sides of equation 1 by 6 and equation 2 by 18 to make the coefficients of y the same:
1) 6(17x + 18y) = 6(582.53) => 102x + 108y = 3495.18
2) 18(28x + 6y) = 18(582.72) => 504x + 108y = 10490.16
Now, subtract equation 1 from equation 2 to eliminate y:
(504x + 108y) - (102x + 108y) = 10490.16 - 3495.18
402x = 6994.98
Now, solve for x:
x = 6994.98 / 402
x ≈ 17.43
Now that we have the value of x, we can substitute it back into equation 1 to find y:
17(17.43) + 18y = 582.53
296.31 + 18y = 582.53
18y = 582.53 - 296.31
18y = 286.22
y = 286.22 / 18
y ≈ 15.90
So, the cost of a ribeye steak dinner is approximately $17.43, and the cost of a grilled salmon dinner is approximately $15.90.