Unless you have gobs of money and can hook your child up with some pick up/drop off laundry service, or unless your child can get some poor schlub to do their laundry for them, it's just an unavoidable chore.
$53: Pop-up hamper ($12), laundry backpack ($10), 2 mesh wash bags ($10), Tide free of dyes and perfumes, 50 oz. ($12), Seventh Generation dryer sheets, free and clear ($9) -- bedbathandbeyond.com
$20: Compact accordion drying rack -- bedbathandbeyond.com
$50: Rowenta Effective Comfort Iron, with auto shut off ($40), plus ironing board ($10) -- bedbathandbeyond.com
The tally: $4,995.50