Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. For her parents' anniversary party, Maddie is considering using one of two venues. A hotel in Springfield will cost $269 for a reservation, plus $28 per person. A restaurant in the same city will cost $30 per person, in addition to $267 for the reservation. In order to make the best decision, Maddie 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 $_____.

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, Maddie is considering using one of two venues. A hotel in Springfield will cost $269 for a reservation, plus $28 per person. A restaurant in the same city will cost $30 per person, in addition to $267 for the reservation. In order to make the best decision, Maddie 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 $_____.

Bytelearn · Accepted Answer

Define variables: Let's define the variables. Let x be the number of attendees, and let C be the total cost for either venue.Write hotel equation: Write the equation for the hotel in Springfield. The cost is $269 for the reservation plus $28 per person. C = 269 + 28xWrite restaurant equation: Write the equation for the restaurant in the same city. The cost is $267 for the reservation plus $30 per person. C = 267 + 30xSet equations equal: Set the two equations equal to each other to find the number of attendees for which the cost is the same. 269 + 28x = 267 + 30xSolve for x: Solve for x by subtracting 28x from both sides of the equation. 269 + 28x - 28x = 267 + 30x - 28x 269 = 267 + 2xIsolate variable x: Subtract 267 from both sides to isolate the variable x. 269 - 267 = 267 + 2x - 267 2 = 2xDivide to solve x: Divide both sides by 2 to solve for x. 2 / 2 = 2x / 2 1 = xCalculate total cost: Now that we have the number of attendees (x), we can calculate the total cost (C) for either venue. C = 269 + 28(1) = 269 + 28 = 297 C = 267 + 30(1) = 267 + 30 = 297

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