Model for Bobo and the Wedding Reception

I.  Problem Statement

     How many people can be seated if they have 20, 50, 100 or n tables?

II.  Procedure

     The information given is that the table must be continuous, and it will consist of triangular tables with one seat on each side.  We don't need to know anything else.  I tried drawing a picture, making a table, looking for a pattern, and writing an equation.

     First, we drew a picture of how the tables would be arranged and put the resulting data into a table.  The table had "number of tables" on the left side and "seat" on the right side.  From my drawing I saw that one table would have 3 seats, 2 tables would have 4 seats, 3 tables would have 5 seats, and 4 tables would have 5 seats.  I filled in both sides of the table with my data.

     Then I looked at the pattern in the table and saw that the right side increased by 1 each time.  I also added a 0 step to my table and saw that the right side there would be 2.  Because I know that the interval is the coefficient of the variable and the 0 step is added to the variable, I concluded that the equation would be s = t + 2.

     I made a graph from my data by numbering along the horizontal axis for the number of tables and numbering up along the vertical axis for the number of seats.  I plotted the points from my table and extended the line. 

     I solved the equation for t = 20, t = 50, t = 100 by plugging those numbers into s = t + 2, and I got 22, 52, and 102.

III. Observations

     Table, graph, function rule, equations solved.

IV.  Conclusions

     With 20 tables there would be 22 seats, with 50 tables there would be 52 seats, with 100 tables there would be 102 seats, and with n tables there would be n + 2 seats.

     The results were what I expected.

     The results turned out as they did because when you put the tables next to each other you lose one side on each table, resulting in only 2 sides available for seating.