How Many Attendees?

Question

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

An event organizer is reserving rooms for two company-wide events. For the quarterly meeting this month, she reserved 1 conference room and 3 ballrooms, which can seat a total of 233 attendees. For safety training next month, she reserved 2 conference rooms and 3 ballrooms, which can seat 253 attendees. How many attendees can each room accommodate?

Each conference room can accommodate ___ attendees, and every ballroom can accommodate ___ attendees.

Answer 1

C + 3b = 233

2C + 3B = 253

Subtracting: 2C - C = 253 - 233

C = 20

Per first equation:

20 + 3b = 233

3b = 213

b = 71

conference room seats 20.

ballroom seats 71