Alina and her best friend Lucia like to chat a lot. On a particular day, Alina sent 20 fewer messages than her friend Lucia, who sent 120 messages. The next day, Lucia sent 1/3 of the messages she sent the previous day, while Alina doubled the messages she sent on the first day. If they sent the same number of messages on the third day as the first day, what is the total number of messages they sent in those three days?
On the first day, Alina sent 120 - 20 = <<120-20=100>>100 messages.
The total number for the first day is 100+120 = <<100+120=220>>220 messages.
On the second day, Lucia sent 1/3 *120 = <<1/3*120=40>>40 messages.
Alina sent 100*2 = <<100*2=200>>200 messages on the second day.
The total for the second day is 40+200 = <<40+200=240>>240 messages.
For the three days, they sent 220+220+240 = <<220+220+240=680>>680 messages.
#### 680