A waitress sold 18 ribeye steak dinners and 15 grilled salmon dinners, totaling $573.79 on a particular day. Another day she sold 24 ribeye steak dinners and 5 grilled
salmon dinners, totaling $580.18. How much did each type of dinner cost?
Let's assume the cost of a ribeye steak dinner is x, and the cost of a grilled salmon dinner is y.
According to the problem, we have the following equations:
18x + 15y = 573.79 ........(1)
24x + 5y = 580.18 ........(2)
Multiplying equation (2) by 3, we get:
72x + 15y = 1740.54 .......(3)
Now we can subtract equation (1) from equation (3) to eliminate y:
72x + 15y - (18x + 15y) = 1740.54 - 573.79
54x = 1166.75
x = 1166.75 / 54
x = 21.60
Substituting the value of x in equation (1), we can find y:
18(21.60) + 15y = 573.79
388.80 + 15y = 573.79
15y = 573.79 - 388.80
15y = 184.99
y = 184.99 / 15
y = 12.33
So, the cost of a ribeye steak dinner is $21.60 and the cost of a grilled salmon dinner is $12.33.
Let's assume the cost of a ribeye steak dinner is x dollars and the cost of a grilled salmon dinner is y dollars.
Based on the information given, we can set up a system of equations to solve for x and y:
18x + 15y = 573.79 -- (Equation 1)
24x + 5y = 580.18 -- (Equation 2)
To solve this system of equations, we can use the method of elimination.
Multiply Equation 1 by 24 and Equation 2 by 18 to eliminate x:
(18x + 15y) * 24 = 573.79 * 24
(24x + 5y) * 18 = 580.18 * 18
432x + 360y = 13749.96 -- (Equation 3)
432x + 90y = 10443.24 -- (Equation 4)
Now, subtract Equation 4 from Equation 3 to eliminate x:
(432x + 360y) - (432x + 90y) = 13749.96 - 10443.24
432x - 432x + 360y - 90y = 3312.72
270y = 3312.72
Divide both sides of the equation by 270:
y = 3312.72 / 270
y ≈ 12.27
So, the cost of a grilled salmon dinner is approximately $12.27.
Now, substitute this value back into Equation 1 to solve for x:
18x + 15(12.27) = 573.79
18x + 183.9 = 573.79
18x = 573.79 - 183.9
18x = 389.89
Divide both sides of the equation by 18:
x = 389.89 / 18
x ≈ 21.66
Therefore, the cost of a ribeye steak dinner is approximately $21.66.
In conclusion, the ribeye steak dinner costs approximately $21.66 and the grilled salmon dinner costs approximately $12.27