Problem:
Sally has booked hotel rooms for her wedding. There are twice as many small rooms as there are large rooms. Small rooms hold 2 people and large rooms hold 5 people. 63 people booked rooms for her wedding and the rooms were booked to capacity. How many of them were small rooms and how many of them were large rooms?
Solution:
Known: There are twice as many small rooms as large rooms. Let S be small rooms and L be large rooms. So S = 2L.
We also know that 63 people were in the rooms (filled to capacity) and how many are in each type of room (2 for small, 5 for large). So, 5L + 2S = 63.
Now, since we know S = 2L, we can rewrite the problem:
5L + 2(2L) = 63
Now solve:
5L + 4L = 63
9L = 63
L =63
9
L = 7
S = 2L = 2(7) = 14
So, there were 7 large rooms and 14 small rooms booked.