Question

Dominic 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 6 people. Dominic booked a total of 22 rooms which can accommodate 108 guests altogether. Graphically solve a system of equations in order to determine the number of small rooms reserved, x, commax, and the number of large rooms reserved, yy.

Answer 1

Answer: 8 small rooms and 14 large rooms

Explanation:

Define the Variables:

Let's use

x for the number of small rooms booked (each for 3 people).

Let's use

y for the number of large rooms booked (each for 6 people).

Write the Equations:

The first equation represents the total number of rooms booked:

x+y=22.

The second equation represents the total number of guests:

3x+6y=108.

Graph the Equations:

First, plot the line

x+y=22. This line represents all possible combinations of small and large rooms that add up to 22 rooms.

Second, plot the line

3+6=108

3x+6y=108. This line represents all possible combinations of small and large rooms that accommodate 108 guests.

Find the Intersection Point:

The point where the two lines intersect on the graph represents the solution. It's the combination of small and large rooms that fulfill both conditions (number of rooms and number of guests).

Interpret the Solution:

Look at the coordinates of the intersection point. The x-coordinate tells us how many small rooms are booked, and the y-coordinate tells us how many large rooms are booked.

Remember, the solution represents the number of small rooms (x) and the number of large rooms (y) Dominic booked for his guests coming to the wedding.