Question

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.

Answer 1

Answer:

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

$2x+5y=85$

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

$y=3x$

3. Substitute the secons equation into the first one:

$2x+5\cdot 3x=85\\ \\2x+15x=85\\ \\17x=85\\ \\x=5\\ \\y=3x=3\cdot 5=15$

Answer 2

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

• $2s + 5l = 85$ -- the total number of guests
• $l =3s$ -- the relationship between the two sizes of rooms

Substitute 3s for l in $2s + 5l = 85$

$2s + 5(3s) = 85$

Open bracket

$2s + 15s = 85$

Evaluate like terms

$17s = 85$

Divide both sides by 17

$s = 5$

Substitute 5 for s in $l =3s$

$l =3 \times 5$

$l =15$

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

Read more about linear functions at:

https://brainly.com/question/15602982