Question

Austin is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 2 people, and large rooms that can hold 3 people. Austin booked a total of 22 rooms which can accommodate 53 guests altogether. Determine the number of small rooms reserved and the number of large rooms reserved.

Answer 1

There are 13 small rooms and 9 large rooms reserved.

Explanation:

First, we can make a system of equations. We can use s to represent the number of small rooms and l to represent the number of large rooms.

2 guests per small room added to 3 guests per large room equals 53 guests total, so 2s + 3l = 53.

The number of small rooms (s) plus the number of large rooms (l) equals the total number of rooms, so s + l = 22 or s = 22 - l.

We can substitute the first second equation into the first equation.

2 (22 - l) + 3l = 53

44 - 2l + 3l = 53

l = 9

So, the number of large rooms is 9. Then, to find the number of small rooms, we can substitute l into the second equation.

s = 22 - 9

s = 13

So, the number of small rooms is 13.