Question

Hudson 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 6 people. Hudson booked a total of 19 rooms which can accommodate 87 guests altogether. 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.

Answer 1

Our system is : S + L = 19, and 3S + 6L = 87

Let # of small rooms = S

# of Large rooms = L

10 Large rooms and 9 Small rooms

Explanation:

Let # of small rooms = S

# of Large rooms = L

S + L = 19

3*S + 6*L = 87

Our system is : S + L = 19, and 3S + 6L = 87

solve.

S = 19 - L

3*(19 - L) + 6L = 87

57 - 3L + 6L = 87

57 + 3L = 87

3L = 30

L = 10

S = 19 - 10 = 9

Answer 2

Explanation:

Let the number of smaller rooms be x

Total rooms are 19. So, number of larger rooms = 19 - x

Total guests = 87

3x + (19-x)6 = 87