Question

A waitress sold 11 ribeye steak dinners and 14 grilled salmon dinners, totaling $551.11 on a particular day. Another day she sold 15 ribeye steak dinners and 7 grilled salmon dinners, totaling $581.47. How much did each type of dinner cost?

Answer 1

A ribeye steak dinner costs $32.23 and a grilled salmon dinner costs $14.04.

Explanation:

Let's use variables to represent the cost of each dinner. Let's say that the cost of a ribeye steak dinner is "r" and the cost of a grilled salmon dinner is "s".

From the first day's sales, we know:

• 11r + 14s = 551.11

From the second day's sales, we know:

• 15r + 7s = 581.47

We now have two equations with two variables, which we can solve using elimination or substitution.

Let's use elimination. If we multiply the first equation by 15 and the second equation by 11, we can eliminate the "r" variable:

• 165r + 210s = 8266.65
• 165r + 77s = 6396.17

Subtracting the second equation from the first, we get:

• 133s = 1870.48

Dividing both sides by 133, we get:

• s = 14.04

So a grilled salmon dinner costs $14.04.

We can substitute this value back into one of the original equations to solve for "r". Let's use the first equation:

• 11r + 14(14.04) = 551.11
• 11r + 196.56 = 551.11
• 11r = 354.55
• r = 32.23

So a ribeye steak dinner costs $32.23.

Therefore, a ribeye steak dinner costs $32.23 and a grilled salmon dinner costs $14.04.