Question

José is blocking off several rooms in a hotel for guest coming to his wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4 people. Jose reserved twice as many small rooms as large rooms, which altogether can accommodate 70 guest. 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 the variables that you use to write the system

Answer 1

`x=2y\,,\,3x+4y=70` where x denotes number of small rooms and y denotes number of large rooms

Explanation:

Given: Small rooms can hold 3 people, and large rooms can hold 4 people.

Number of small rooms is twice the number of large rooms.

Small rooms and large rooms altogether can accommodate 70 guests.

To find: system of equations that could be used to determine the number of small rooms reserved and the number of large rooms reserved

Solution:

Let x denotes number of small rooms and y denotes number of large rooms.

As number of small rooms is twice the number of large rooms,

`x=2y`

As small rooms and large rooms altogether can accommodate 70 guests such that small rooms can hold 3 people, and large rooms can hold 4 people,

`3x+4y=70`