Question

For his parents' anniversary party, Roy is considering using one of two venues.

A hotel in Stafford will cost $500 for a reservation, plus $4 per person. A
restaurant in the same city will cost $7 per person, in addition to $200 for the
reservation. In order to make the best decision, Roy figures out how many
attendees it would take to have the venues cost the same amount. What
would the total cost be?

Answer 1

Let's assume that the number of attendees for the party is "x". We want to find the number of attendees for which the cost of the two venues will be the same.

The cost of the hotel in Stafford can be expressed as:

Total cost of the hotel = $500 + $4x

The cost of the restaurant can be expressed as:

Total cost of the restaurant = $200 + $7x

To find the number of attendees for which the cost of the two venues will be the same, we can set the two equations equal to each other and solve for x:

$500 + $4x = $200 + $7x

$500 - $200 = $7x - $4x

$300 = $3x

x = 100

Therefore, if the number of attendees is 100, the total cost of the hotel and the restaurant will be the same. To find the total cost, we can substitute x=100 into either equation:

Total cost = $500 + $4(100) = $900 (for the hotel)

or

Total cost = $200 + $7(100) = $900 (for the restaurant)

Therefore, the total cost for either venue when the number of attendees is 100 is $900.