Question

Write a system of equations to describe the situation below, solve using substitution, and fillin the blanks.For her parents' anniversary party, Laura is considering using one of two venues. A hotel in Dayton will cost $693 for a reservation, plus $51 per person. A restaurant in the same city will cost $60 per person, in addition to $684 for the reservation. In order to make the best decision. Laura figures out how many attendees it would take to have the venues cost thesame amount. How many attendees would that be? What would the total cost be?

Answer 1

• The number of attendees = 1

,

• Total Cost = $744

Step-by-step explanation:

Let the number of attendees = n

A hotel in Dayton will cost $693 for a reservation, plus $51 per person.

`\text{ Hotel's Cost, H\lparen n\rparen}=693+51n\cdots(1)`

A restaurant will cost $60 per person, in addition to $684 for the reservation.

`\text{ Restaurant's Cost, R\lparen n\rparen}=684+60n\cdots(2)`

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:

`693+51n=684+60n`

Solve the equation for n:

`\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} \\ (9)/(9)=(9n)/(9) \\ n=1 \end{gathered}`

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:

`\begin{gathered} \begin{equation*} 693+51n\cdots(1) \end{equation*} \\ Total\text{ Cost}=693+51(1)=\$744 \end{gathered}`

The total cost will be $744.