Question

Eli 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. Eli reserved twice as many large rooms as small rooms, which altogether can accommodate 65 guests. Determine the number of small rooms reserved and the number of large rooms reserved.

Answer 1

Answer: 5 small rooms and 10 large rooms.

Explanation:

Let be "s" the number of small rooms reserved and "l" the number of large rooms reserved.

Using the information given in the exercise, set up a System of equations:

`\left \{ {{3s+5l=65} \atop {l=2s}} \right.`

Now, in order to solve the System of equations, you can use the Substitution method. The steps are:

1. You must substitute the second equation into the first equation:

`3s+5l=65\\\\3s+5(2s)=65`

2. Now, you must solve for the variable "s" in order to find its value:

`3s+5(2s)=65\\\\3s+10s=65\\\\13s=65\\\\s=5`

3. Finally, substitute the value of "s" into the second equation and evaluate, in order to find the value of "l". You get that this is:

`l=2s\\\\l=2(5)\\\\l=10`