That's all very interesting, but you haven't said WHY you're telling us all of that.
I have a hunch, and I'm going with my gut ... Unless I miss my guess. I suppose now you want us to tell you what "the number" actually is. OK. Watch closely.
We don't know what the number is, but in order to work with it, we need something to CALL IT. I'll call it " Q " .
-- the number . . . Q
-- eight times the number . . . 8Q
-- 20 less than eight times the number . . . 8Q - 20
-- 15 more than the number . . . Q + 15
So you just said that (8Q - 20) = (Q + 15) , and now we can 'solve' this for Q .
Start with (8Q - 20) = (Q + 15)
Take that, and subtract Q from each side:
7Q - 20 = 15
Take that, and add 20 to each side:
7Q = 35
Take that, and divide each side by 7 :
Q = 5 <== There's your mystery number.