Question

Emily 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 3 people. Emily booked a total of 15 rooms which can accommodate 36 guests altogether. Graphically solve a system of equations in order to determine the number of small rooms reserved, x,, and the number of large rooms reserved, y

Answer 1

She booked 9 small rooms and 6 large rooms

Explanation:

Let x be the number of small rooms and y be the number of large rooms:

2x+3y=36

x+y=15

Multiply the second equation by 2:

2x+2y=30

2x+3y=36 (Rewriting this for clarity purposes)

Subtract the second equation from the first equation:

-y=-6

y=6

Plug 6 back in for y

x+6=15

x=9

She booked 9 small rooms and 6 large rooms