Question

question nolan 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 5 people. nolan booked a total of 25 rooms which can accommodate 99 guests altogether. determine the number of small rooms reserved and the number of large rooms reserved. answer attempt 1 out of a there were small rooms reserved and large rooms reserved. submit answer

Explanation:

Step1: Define variables

Let \( x \) be the number of small rooms and \( y \) be the number of large rooms. We know two equations:

1. \( x + y = 25 \) (total number of rooms)
2. \( 3x + 5y = 99 \) (total number of guests)

Step2: Solve the system of equations

From the first equation, we can express \( x \) as \( x = 25 - y \). Substitute this into the second equation:

$$ 3(25 - y) + 5y = 99 $$

$$ 75 - 3y + 5y = 99 $$

$$ 75 + 2y = 99 $$

$$ 2y = 99 - 75 $$

$$ 2y = 24 $$

$$ y = 12 $$

Step3: Find \( x \)

Substitute \( y = 12 \) into \( x = 25 - y \):

$$ x = 25 - 12 = 13 $$

Answer:

There were \(\boldsymbol{13}\) small rooms reserved and \(\boldsymbol{12}\) large rooms reserved.