For her parents' anniversary party, Mary is considering using one of two venues. A hotel in Newton will cost $823 for a reservation, plus $42 per person. A restaurant in the same city will cost $82 per person, in addition to $663 for the reservation. In order to make the best decision, Mary 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 total cost would be $991.

The number of attendees would be 4.

Step-by-step explanation:

Let 'x' be the number of attendees,

Total cost = Reservation + cost of all attendees. Total cost of 1st Hotel = $823 + $42x Total cost of 2nd Hotel = $663 + $82x

To have the venues cost the same amount,

$823 + $42x = $663 + $82x

⇒ $823 - $663 = $82x - $42x

⇒ 160 = 40x

⇒ x = 160/40

⇒ x = 4 attendees.

Substitute x=4 to find the total cost.

⇒ $823 + $42 (4) = $991

⇒ $663 + $82 (4) = $991

∴ The cost for the two venues are same.