You raise to $6. The button calls and both blinds fold, leaving $1 and $2 in the pot.
You bet $5, a third of the pot. The button calls.
You check, because a call on the flop can mean a queen. The button checks too, which makes a queen less likely.
You check and the button bets $12. You'd pay $12 to win $37, so you need to win 12 / 49, or 1 time in 4. They checked the turn, so you call. They show king-ten.
You take the $49 pot, and you put in $23 of it: $6, $5 and $12.