Respuesta :
Solution:
Given:
[tex]\text{Total expected guests=45}[/tex]To seat an equal number of guests at each table with each table having more than one guest, then the following applies.
[tex]\begin{gathered} \text{Factors of 45=1,3,5,9,15,45} \\ \text{This means the number of guests at each table are the factors. But 1 is not included since a table must have more than one guest} \end{gathered}[/tex]Part A:
The different ways the guests and tables could be arranged are;
[tex]\begin{gathered} 3\text{guests per table with }15\text{tables} \\ 5\text{guests per table with }9\text{tables} \\ 9\text{guests per table with }5\text{tables} \\ 15\text{guests per table with }3\text{tables} \\ 45\text{guests per table with 1table} \end{gathered}[/tex]Part B:
Jordan and Mitchell forgot to include themselves.
With the two of them inclusive, the total number becomes 47.
Since 47 is a prime number, the factors of 47 are 1 and 47.
Hence, to have an equal number of guests at the table, with Jordan and Mitchell included,
[tex]\begin{gathered} \text{All 47 of them wll be together on 1 table} \\ \text{This is the only possibility when they are 47 to maintain the condition of having more than one guest on each table as well as having equal number of guests at each table.} \\ \\ \text{Thus, 47 guests with 1 table is the way to arrange with Jordan and Mitchell inclusive.} \\ 47\text{guests per table with 1table} \end{gathered}[/tex]