Question

A waitress sold 13 ribeye steak dinners and 12 grilled salmon dinners, totaling $592.87 on a particular dayAnother day she sold 18 ribeye steak dinners and 6 grilled salmon dinners, totaling $580.21. How much did each type of dinner cost?

The cost of ribeye steak dinners is
And the cost of salmon dinners is

Answer 1

Explanation:

Let's use a system of equations to solve for the cost of each type of dinner.

Let x be the cost of ribeye steak dinners and y be the cost of grilled salmon dinners.

From the first day's sales, we can write:

13x + 12y = 592.87

And from the second day's sales, we can write:

18x + 6y = 580.21

We now have two equations with two variables. We can solve for one variable in terms of the other in either equation, and then substitute that expression into the other equation to solve for the remaining variable.

Solving the first equation for y, we get:

y = (592.87 - 13x) / 12

Substituting this expression into the second equation, we get:

18x + 6[(592.87 - 13x) / 12] = 580.21

Simplifying and solving for x, we get:

x = 28.95

Substituting this value of x back into the first equation to solve for y, we get:

y = 23.56

Therefore, the cost of ribeye steak dinners is $28.95 and the cost of grilled salmon dinners is $23.56.