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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.The owner of a new restaurant is designing the floor plan, and he is deciding between two different seating arrangements. The first plan consists of tables and booths, which will seat a total of people. The second plan consists of tables and booths, which will seat a total of people. How many people can be seated at each type of table?Every table can seat _____ people, and every booth can seat _____ people.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.The owner of a new restaurant is designing the floor plan, and he is deciding between two different seating arrangements. The first plan consists of tables and booths, which will seat a total of people. The second plan consists of tables and booths, which will seat a total of people. How many people can be seated at each type of table?Every table can seat _____ people, and every booth can seat _____ people.
- Define Equations: Let's denote the number of people that can be seated at a table as and the number of people that can be seated at a booth as . We can then write two equations based on the given information.First plan: Second plan:
- Create System: We have a system of linear equations:To solve the system, we can subtract the first equation from the second to eliminate .
- Eliminate Variable: Perform the subtraction to find the value of .Now, divide both sides by to solve for .
- Solve for T: Now that we have the value for , we can substitute it back into one of the original equations to solve for . Let's use the first plan's equation:
- Substitute and Solve: Subtract from both sides to solve for . Now, divide both sides by to find the value of .
