Prove that if a point in the interior of an angle is equidistant from the sides of the angle then it belongs to the angle bisector of the angle (Point on angle bisector converse theorem).

Ashley spent half of her lunch money on a turkey sandwich. then she spent two-thirds of the money she had left on a bottle of juice and the rest of the money on a cookie. if the cookie cost $.75, how much lunch money did ashley have to start with?