Lucy is blocking off several rooms in a hotel for guests coming to her wedding. the hotel can reserve small rooms that can hold 2 people, and large rooms that can hold 5 people. lucy reserved 3 times as many large rooms as small rooms, which altogether can accommodate 85 guests. determine the number of small rooms reserved and the number of large rooms reserved.

The proportion of small and large rooms is an illustration of linear functions

Lucy should reserve 3 small rooms, and 15 large rooms

Represent small rooms with s, and large rooms with l.

So, we have the following system of equations

Substitute 3s for l in

Open bracket

Evaluate like terms

Divide both sides by 17

Substitute 5 for s in

Hence, Lucy should reserve 3 small rooms, and 15 large rooms

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5 small rooms and 15 large rooms

Step-by-step explanation:

Let

x = number of small rooms

y = number of large rooms

1. Small rooms can hold 2 people, so there are 2x people in x small rooms. Large rooms can hold 5 people, so there are 5y in y large rooms.

In total, there are 2x + 5y people in all rooms.

All rooms can accommodate 85 guests, so

2. Lucy reserved 3 times as many large rooms as small rooms, so

3. Substitute the secons equation into the first one: