Respuesta :
Answer:
• The number of attendees = 1
,• Total Cost = $744
Explanation:
Let the number of attendees = n
A hotel in Dayton will cost $693 for a reservation, plus $51 per person.
[tex]\text{ Hotel's Cost, H\lparen n\rparen}=693+51n\cdots(1)[/tex]A restaurant will cost $60 per person, in addition to $684 for the reservation.
[tex]\text{ Restaurant's Cost, R\lparen n\rparen}=684+60n\cdots(2)[/tex]We want to find the number of attendees(n) at which the venues cost the same amount.
Equate the cost equations (1) and (2) above:
[tex]693+51n=684+60n[/tex]Solve the equation for n:
[tex]\begin{gathered} \text{Subtract 51n from both sides of the equation.} \\ 693+51n-51n=684+60n-51n \\ 693=684+9n \\ \text{Subtract 684 from both s}\imaginaryI\text{des of the equat}\imaginaryI\text{on} \\ 693-684=684-684+9n \\ 9=9n \\ \text{ Divide both sides by 9} \\ \frac{9}{9}=\frac{9n}{9} \\ n=1 \end{gathered}[/tex]The number of attendees it would take for the cost to be the same amount is 1.
We determine the total cost using any of the equations:
[tex]\begin{gathered} \begin{equation*} 693+51n\cdots(1) \end{equation*} \\ Total\text{ Cost}=693+51(1)=\$744 \end{gathered}[/tex]The total cost will be $744.
