Answer
The owner charges $55 per haircut.
Work Step by Step
$x+20 = y$
$12x+6y = 750$
$12x+6*(x+20) = 750$
$12x+6x+120 = 750$
$18x +120 =750$
$18x+120-120 = 750 -120$
$18x = 630$
$18x/18 = 630/18$
$x = 35$
$x+20 = y$
$35 + 20= 55= y$