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A waitress sold 20 ribeye steak dinners and 12 grilled salmon​ dinners, totaling ​$559.11 on a particular day. Another day she sold 29 ribeye steak dinners and 6 grilled salmon​ dinners, totaling ​$583.72 How much did each type of dinner​ cost?

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jessmzhou4

Answer:

  • Ribeye steak dinner ≈ $16.01
  • Grilled salmon dinner ≈ $19.91

Explanation:

  • Number of ribeye steak dinners sold = x
  • Number of grilled salmon dinners sold = y

Create two equations showing the amount sold and earned each day:

[tex]\left \{ {{20x+12y=559.11} \atop {29x+6y=583.72}} \right.[/tex]

Solve the system of equations:

[tex]\left \{ {{20x+12y=559.11} \atop {29x+6y=583.72}} \right.\\\\=\left \{ {{20x+12y=559.11} \atop {29(2)x+6(2)y=583.72(2)}} \right.\\\\=\left \{ {{20x+12y=559.11} \atop {58x+12y=1167.44}} \right.\\\\(20-58)x+(12-12)y=559.11-1167.44\\\\-38x=-608.33\\\\x=\frac{-608.33}{-38} =16.01\\\\20x+12y=559.11\\20(16.01)+12y=559.11\\12y=559.11-20(16.01)\\12y=238.91\\y=19.91[/tex]

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