Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

For her parents' anniversary party, Vera is considering using one of two venues. A hotel in Stamford will cost $569 for a reservation, plus $56 per person. A restaurant in the same city will cost $54 per person, in addition to $811 for the reservation. In order to make the best decision, Vera figures out how many attendees it would take to have the venues cost the same amount. How many attendees would that be? What would the total cost be?

If the party had ___ attendees, the cost at each venue would be $ ___.

 Jan 21, 2019

We have: \(56x+569=54x+811\) . So, \(2x=242\), and \(x=121\)


The total cost is \(56(121)+569=7345.\)


If the party had \(\boxed{121}\) attendees, the cost at each venue would be \(\boxed{\$7345}\)

 Jan 21, 2019

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