A waitress sold 18 ribeye steak dinners and 12 grilled salmon dinners, totaling $563.44 on a particular day. Another day she sold 26 ribeye steak dinners and 6 grilled salmon dinners, totaling $580.72. How much did each type of dinner cost?

Question

A waitress sold 18 ribeye steak dinners and 12 grilled salmon dinners, totaling  $563.44 on a particular day. Another day she sold 26 ribeye steak dinners and 6 grilled salmon dinners, totaling  $580.72. How much did each type of dinner cost?

Bytelearn · Accepted Answer

Set up equations: Let's denote the cost of a ribeye steak dinner as R and the cost of a grilled salmon dinner as S. We can set up two equations based on the information given: 1) 18R + 12S = $563.44 2) 26R + 6S = $580.72 These equations represent the total sales for each type of dinner on two different days.Use elimination method: We can use the method of substitution or elimination to solve this system of equations. Let's use the elimination method. We'll multiply the second equation by 2 to make the coefficient of S in both equations the same: 2 * (26R + 6S) = 2 * $580.72 This gives us: 52R + 12S = $1161.44Subtract equations: Now we have the system of equations: 1) 18R + 12S = $563.44 2) 52R + 12S = $1161.44 We can subtract the first equation from the second to eliminate S: (52R + 12S) - (18R + 12S) = $1161.44 - $563.44 This simplifies to: 34R = $598.00Solve for R: Now we can solve for R by dividing both sides of the equation by 34: 34R / 34 = $598.00 / 34 R = $17.59 So, the cost of a ribeye steak dinner is $17.59.Substitute back for S: Now that we have the value of R, we can substitute it back into one of the original equations to find the value of S. Let's use the first equation: 18R + 12S = $563.44 Substituting the value of R gives us: 18($17.59) + 12S = $563.44 Calculating 18 times $17.59 gives us: $316.62 + 12S = $563.44Now we can solve for S by subtracting $316.62 from both sides of the equation: 12S = $563.44 - $316.62 12S = $246.82 Dividing both sides by 12 gives us: S = $246.82 / 12 S = $20.57 So, the cost of a grilled salmon dinner is $20.57.

A waitress sold $18$ ribeye steak dinners and $12$ grilled salmon dinners, totaling $\$ 563.44$ on a particular day. Another day she sold $26$ ribeye steak dinners and $6$ grilled salmon dinners, totaling $\$ 580.72$ . How much did each type of dinner cost?

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A waitress sold 181818 ribeye steak dinners and 121212 grilled salmon dinners, totaling $563.44 \$ 563.44 $563.44 on a particular day. Another day she sold 262626 ribeye steak dinners and 666 grilled salmon dinners, totaling $580.72 \$ 580.72 $580.72. How much did each type of dinner cost?

A waitress sold $18$ ribeye steak dinners and $12$ grilled salmon dinners, totaling $\$ 563.44$ on a particular day. Another day she sold $26$ ribeye steak dinners and $6$ grilled salmon dinners, totaling $\$ 580.72$ . How much did each type of dinner cost?