Question

Alexander is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4 people. Alexander reserved 4 more large rooms than small rooms, which altogether can accommodate 58 guests. Determine the number of small rooms reserved and the number of large rooms reserved.

Answer 1

Small rooms=6

large rooms=10

Explanation:

Let the number of small rooms be x

given alexander booked 4 more large rooms than the small rooms.

Therefore the number of large numbers be x+4.

Given each small room can accommodate 3 people.Therefore the total number of people in small rooms are 3x

Given each large room can accommodate 4 people. Therefore the total number of people in large rooms are 4(x+4)

Given total number of people accommodated=58

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

`58=3x+4(x+4)`

`7x=42`

`x=6`

therefore the number of small rooms =6 and number of large rooms =10