Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. For her parents' anniversary party, Sandra is considering using one of two venues. A hotel in Newport will cost $659 for a reservation, plus $97 per person. A restaurant in the same city will cost $98 per person, in addition to $658 for the reservation. In order to make the best decision, Sandra figures out how many attendees it would take to have the venues cost the same amount. What would the total cost be? How many attendees would that be? The cost at each venue would be $_____ if the party had _____ attendees.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  For her parents' anniversary party, Sandra is considering using one of two venues. A hotel in Newport will cost $659 for a reservation, plus $97 per person. A restaurant in the same city will cost $98 per person, in addition to $658 for the reservation. In order to make the best decision, Sandra figures out how many attendees it would take to have the venues cost the same amount. What would the total cost be? How many attendees would that be?   The cost at each venue would be $_____ if the party had _____ attendees.

Bytelearn · Accepted Answer

Set up equations: Set up the equations for the cost of each venue. The hotel in Newport costs $659 for a reservation plus $97 per person. If we let x represent the number of attendees, then the cost for the hotel can be represented by the equation: Cost_hotel = 659 + 97x The restaurant costs $658 for a reservation plus $98 per person. The cost for the restaurant can be represented by the equation: Cost_restaurant = 658 + 98xSet equal and solve: Set the two costs equal to each other to find the number of attendees for which the costs are the same. 659 + 97x = 658 + 98xFind total cost: Solve for x by subtracting 97x from both sides of the equation and subtracting 658 from both sides. 659 + 97x - 97x = 658 + 98x - 97x 659 - 658 = 98x - 97x 1 = xDetermine the total cost for each venue when x equals 1. Cost_hotel = 659 + 97(1) = 659 + 97 = 756 Cost_restaurant = 658 + 98(1) = 658 + 98 = 756

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