15 guests
Explanation:
The cost for 6 guest = $30
let the cost per guest = x
[tex]\begin{gathered} 6\times\text{ x = 30} \\ 6x\text{ = 30} \\ x\text{ = 30/6 } \\ x\text{ = 5} \end{gathered}[/tex]The cost per guest = x = $5
when the total cost = $75
let number of guest for the $75= y
[tex]\begin{gathered} nu\text{mber of guest }\times\text{ cost per guest = 75} \\ Since\text{ relationship is proportional, the cost per guest will be the same} \\ y\times5\text{ = 75} \\ 5y\text{ = 75} \\ y\text{ = 75/5 } \\ y\text{ = 15 guests} \end{gathered}[/tex]The maximum number of guests there can be if Tim can afford to spend a total of $75 on his retirement party is 15 guests.
