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

Step-by-step explanation:

If we let r and g represent the costs of a ribeye steak dinner and grilled salmon dinner, respectively, the sales figures give rise to two equations.

  17r +15g = 553.74

  22r +5g = 582.65

If we multiply the second equation by 3 and subtract the first, we have ...

  3(22r +5g) -(17r +15g) = 3(582.65) -(553.74)

  49r = 1194.21

  r = 1194.21/49 ≈ 24.37

  g = (553.74 -17r)/15 ≈ 9.30

The steak dinner costs $24.37; the salmon dinner costs $9.30.

Check

17(24.37) +15(9.30) = 553.79 . . . not 553.74

22(24.37) +5(9.30) = 582.64 . . . not 582.65

There is no exact solution to this problem.

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