In a trip to Asia a traveler spent $90 a day for hotels in Bangkok, $60 a day in Singapore and $60 a day in Kuala Lumpur. For food the traveler spent $60 a day in Bangkok, $90 a day in Singapore, and $60 a day in Kuala Lumpur. In addition the traveler spent $30 a day in other expenses in each city. The traveler's diary shows that the total hotel bill was $1020, total food bill was $960, and total other expenses were $420. Find the number of days the traveler spent in each city, or show that the diary must be wrong