Question

Evelyn is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 5 people. Evelyn reserved 2 more small rooms than large rooms, which altogether can accommodate 54 guests. Write a system of equations that could be used to determine the number of small rooms reserved and the number of large rooms reserved. Define the variables that you use to write the system

Answer 1

Answer:

Small rooms reserved = 8

Large rooms = 6

Step-by-step explanation:

Let the number of large rooms be x

Evelyn booked 2 more small rooms than the larger rooms.

Therefore the number of small rooms would be x+2.

Given each large room can accommodate 5 people.Therefore the total number of people in large rooms are 5x.

Given each small room can hold 3 people. Therefore the total number of people in large rooms are 3(x+2)

Total number of people accommodated = 54

Total number of guests = total guests in small rooms + total guests in large rooms

$54 = 5x + 3(x+2)\\48 = 8x\\x = 6$

No of large rooms = x = 6

No of small rooms = (x+2) = (6+2) = 8