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

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

No of large rooms = x = 6

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

If the length of a uniform pipe is 45 pounds, then the 18 pound piece is 18/45 the length of the pipe. If 18/45 of the length of the pipe is equal to 3 feet, then we can set up the equation:
(18/45)x = 3ft
Where x is the total length of the pipe. Solving for x:
(18/45)x = 3ft
18x = 135
x = 7.5 feet

We now know that the total length of the pipe before being cut is 7.5 feet. Since the first piece was 3 feet, we know that the second piece must be 4.5 feet (7.5 - 3).

4.5 feet