The school is having a big event in the gym and wants to use their rectangular tables. 6 people can sit together at one rectangular table. If 2 tables are placed together, 10 people can sit together.
So the pattern I noticed is 4 people added whenever a table is added, 1 table 6 people, 2 tables 10 people, 3 tables 14 people, 4 tables 18 people, 5 tables 22 people etc.
The question I have trouble on is this one "Write a mathematical rule that describes the number of people that would sit at n tables. (n stands for any number of tables.) explain how you came up with the rule.
I'm having trouble making a rule from this question, as I don't seem to find an equation to use. What I think is it'll deal with adding four people to each table, whenever a table is added.
6n - 2(n-1) = 4n+2
Thank You!
To come up with a mathematical rule that describes the number of people that would sit at n tables, let's analyze the pattern and break it down step by step:
We have observed that each table holds 6 people, and when 2 tables are placed together, 10 people can sit together. This implies that 4 people are added when another table is added.
If we examine the difference in the number of people between each pair of consecutive table arrangements, we can observe that the difference is constant and equal to 4. This indicates that the relationship between the number of tables (n) and the number of people (P) is a linear relationship.
To find the rule, we need to identify the mathematical relationship using the given pattern. We know that with 1 table, there are 6 people (P = 6), and with 2 tables, there are 10 people (P = 10). Using this information, we can write two equations:
1 table: P = 6
2 tables: P = 10
Now, we want to find the common difference between the two equations to determine the increase from one table arrangement to the next. By subtracting the first equation from the second equation, we have:
(2 tables equation) - (1 table equation):
P(People with 2 tables) - P(People with 1 table) = 10 - 6 = 4
This confirms that adding another table results in an increase of 4 people.
Finally, we can use this information to form the mathematical rule:
P = 4n + 2
In this equation, P represents the number of people and n represents the number of tables.
To explain our reasoning, we started by identifying the pattern and observing the consistent increase of 4 people when adding a table. Then we formed two equations to find the common difference, and finally derived the formula P = 4n + 2 to describe the relationship between the number of tables and the number of people.