A waitress sold 12 ribeye steak dinners and 30 grilled salmon dinners, totaling $557.59 on a particular day. Another day she sold 21 ribeye steak dinners and 10 grilled salmon dinners, totaling $582.75. How much did each type of dinner cost?

Ribeye steak dinner is sold at approximately $23.35 each and grilled salmon dinner costs approximately $9.25 each

Step-by-step explanation:

say ribeye steak dinner is r and grilled salmon dinner is g, we can say

12r + 30g = $557.59 ... eqn 1

21r + 10g = $582.75 ... eqn 2

Multiply eqn 1 by 10 and eqn 2 by 30, so as to eliminate g while solving for r

Then we will have

120r + 300g = $5575.9 ... eqn 3

630r + 300g = $17482.5 ... eqn 4

Subtract eqn 3 from 4 and we will have

510r = $11906.6

Divide both sides by 510 and we will have

r ≈ $23.35

Substitute $23.35 for r in eqn 1 and we will have

12 (23.35) + 30g = 557.59

280.2 + 30g = 557.59

30g = 557.59 - 280.2

30g = 277.39

dividing both sides by 30

g ≈ $9.25