While planning a birthday party for her nephew, Aunt Pat is faced with a problem: which company should she hire to handle the festivities? Patty's Party Patrol charges $30 per hour for a 4-hour party, with a surcharge of $10 for each child after the first eight. Betty's Birthday Bash charges $35 per hour for a 4-hour party, with a $5 surcharge for each child after the first eight. For which number of children will the costs of both party planners be precisely the same? Please explain.