The combined weight of two airline passengers' checked luggage is 105 kilograms. The airline's checked-luggage policy allows each passenger a maximum weight at no charge, and charges a constant, per-kilogram rate for any extra weight. One passenger pays $12.00 for the total extra weight of her luggage, and the other passenger pays $18.00 for the total extra weight of his luggage. If all of the luggage had belonged to one of the passengers, the over-weight charge would have been $78.00. How many kilograms of luggage is one person permitted without charge by the airline?
