A waitress sold 10 ribeye steak dinners and 10 grilled salmon dinners, totaling $584.01 on a particular day. Another day she sold 11 ribeye steak dinners and 5 grilled salmon dinners, totaling $584.45. How much did each type of dinner cost?

Question

A waitress sold 10 ribeye steak dinners and 10 grilled salmon dinners, totaling  $584.01 on a particular day. Another day she sold 11 ribeye steak dinners and 5 grilled salmon dinners, totaling  $584.45. How much did each type of dinner cost?

Bytelearn · Accepted Answer

Set up equations: Let's denote the cost of one ribeye steak dinner as R and the cost of one grilled salmon dinner as S. We can set up two equations based on the information given: 10R + 10S = 584.01 (from the first day's sales) 11R + 5S = 584.45 (from the second day's sales)Simplify first equation: We can simplify the first equation by dividing all terms by 10, which will give us: R + S = 58.401Multiply second equation: Now, let's multiply the second equation by 2 to help us eliminate one of the variables when we subtract the equations: 2(11R + 5S) = 2(584.45) 22R + 10S = 1168.90Align S terms: Next, we multiply the simplified first equation by 10 to align the S terms with the second equation: 10(R + S) = 10(58.401) 10R + 10S = 584.01Eliminate S: Now we subtract the modified first equation from the modified second equation to eliminate S and solve for R: (22R + 10S) - (10R + 10S) = 1168.90 - 584.01 22R - 10R = 1168.90 - 584.01 12R = 584.89Solve for R: Divide both sides by 12 to solve for R: R = 584.89 / 12 R = 48.74Substitute for S: Now that we have the value for R, we can substitute it back into the simplified first equation to solve for S: R + S = 58.401 48.74 + S = 58.401Solve for S: Subtract 48.74 from both sides to solve for S: S = 58.401 - 48.74 S = 9.661

A waitress sold $10$ ribeye steak dinners and $10$ grilled salmon dinners, totaling $\$584.01$ on a particular day. Another day she sold $11$ ribeye steak dinners and $5$ grilled salmon dinners, totaling $\$584.45$ . How much did each type of dinner cost?

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A waitress sold $10$ ribeye steak dinners and $10$ grilled salmon dinners, totaling $\$584.01$ on a particular day. Another day she sold $11$ ribeye steak dinners and $5$ grilled salmon dinners, totaling $\$584.45$ . How much did each type of dinner cost?