Jose 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. Jose reserved twice as many small rooms as large rooms, which altogether can accommodate 70 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.

The number of the small rooms is 14.

The number of large rooms is 7.

Assuming that the number of the large rooms is x,

So, the number of small rooms is 2x

According to the question:

× ×

So, 2x = 2(7) = 14

Therefore, the number of the small rooms is 14 and the number of large rooms is 7.

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No. of large rooms = 7

No. of small rooms = 14

Set of equations

4x + 3y = 70  

y = 2x

Variable definitions

No. of large rooms is x

No. of small rooms is y

Step-by-step explanation:

capacity of large rooms = 4 people

let the no. of large rooms be x

thus, total no of people which can be accommodated in x rooms = 4*x = 4x

capacity of small rooms  = 3 people

let the no. of small rooms be y

thus, total no of people which can be accommodated in y rooms = 3*y = 3y

total no. of people which can be accommodated in x large room and y small room will be = 4x + 3y

It is given that total small room and large room can accommodate 70 guests

thus,

4x + 3y = 70        equation 1

It is also given that Jose reserved twice as many small rooms as large rooms,

so, if no. of large rooms is x  and no. of small rooms is y

then

y = 2x        equation 2

substituting value of y in equation 1 we have

4x + 3(2x) = 70  

=>4x + 6x = 70  

=> 10x = 70

=> x = 70/10 = 7

No. of large rooms = 7

No. of small rooms = y= 2x = 2*7 = 14

Set of equations

4x + 3y = 70  

y = 2x

Variable definitions

No. of large rooms is x

No. of small rooms is y

step-by-step explanation: 4 cause 2+2=4