A waitress sold 10 ribeye steak dinners and 15 grilled salmon​ dinners, totaling ​$584.82 on a particular day. Another day she sold 12 ribeye steak dinners and 5 grilled salmon​ dinners, totaling ​$580.49. How much did each type of dinner​ cost?

Answer 1

Let's assume the cost of a ribeye steak dinner to be x and the cost of a grilled salmon dinner to be y.

According to the given information,
10x + 15y = 584.82 ...(1)
12x + 5y = 580.49 ...(2)

We can now solve these two equations simultaneously to find the values of x and y.

For this, we will multiply equation (1) by 12 and equation (2) by 10 to eliminate the coefficient of x.
120x + 180y = 7017.84 ...(3)
120x + 50y = 5804.9 ...(4)

Now, we will subtract equation (4) from equation (3) to eliminate the x term.
120x - 120x + 180y - 50y = 7017.84 - 5804.9
130y = 1212.94

Dividing both sides of the equation by 130, we get:
y = 9.35

Now, substitute the value of y in equation (2) to find the value of x.
12x + 5(9.35) = 580.49
12x + 46.75 = 580.49
12x = 580.49 - 46.75
12x = 533.74
x = 533.74 / 12
x = 44.48

Therefore, the cost of a ribeye steak dinner is $44.48, and the cost of a grilled salmon dinner is $9.35.