Please help me make sense of this math....

hello,

I was thrown for a total loop today when I went into the doctors. My last missed period was August 4th. I had sex on August 2nd, and then not again until September 14th.

So when I found out I was pregnant in October, they dated me at 10.5 weeks, based on the last missed period. 

However, when I went in today to have an ultrasound today (November 22nd), I thought I was 15 weeks and 5 days. Much to my surprise though, the specialist measured the scan at 10 weeks and 5 days, saying my new due date is June 15th.

They told me I most likely conceived on the 22nd of September, but could have gotten pregnant anywhere within the week of the 15th to the 22nd.... Although when I subtract 10 weeks and 5 days November 22nd, that comes out to September 8th.... and I didn't have sex anywhere around that time.... I was on a backpacking trip and with no one again until the 14th.

From the week of the 14th to the 21st, I had sex everyday.... with the same man except for the 15th, where I got back with my ex. I wasn't dating the guy I was with all the other days.... it is a long and at the moment, irrelevant story.

I am just very confused though, because how on earth do they figure out this math and say that 10 weeks and 5 days ago from November 22nd was September 22nd? I can't make sense of it. I am definitely pregnant, saw the heart beating away, thank goodness, but there's no way it could have happened on the 8th. 

Can anyone help me here?