Violet 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. Violet reserved twice as many large rooms as small rooms, which altogether can accommodate 91 guests. Determine the number of small rooms reserved and the number of large rooms reserved.

Question

Haley Yates

Mathematics

3 July, 07:25

Violet 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. Violet reserved twice as many large rooms as small rooms, which altogether can accommodate 91 guests. Determine the number of small rooms reserved and the number of large rooms reserved.

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Answers (1)

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Nathalia Harding · Answer 1

Violet reserved 7 small room and 14 large rooms in the hotel.

Step-by-step explanation:

Let, the number of small rooms reserved is x and that of the large room reserved is y.

Given that Violet reserved twice as many large rooms as small rooms, which altogether can accommodate 91 guests.

So, y = 2x ... (1)

Again given that small rooms that can hold 3 people, and large rooms that can hold 5 people.

So, 3x + 5y = 91 ... (2)

Now, substituting value of y from equation (1) to equation (2) we get,

3x + 5 (2x) = 91

⇒ 13x = 91

⇒ x = 7

So, from equation (1) we get, y = 2x = 14

Therefore, Violet reserved 7 small room and 14 large rooms in the hotel. (Answer)