Blue = 516 * (1/3) = <<516*(1/3)=172>>172 cars

Red = 516 * (1/2) = <<516*(1/2)=258>>258

Black = 516 - (172 + 258) = 86

There are 86 black cars on the lot.

# Answer

86
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
There are 516 cars in a parking lot. One-third are blue, one-half are red, and the rest are black. How many black cars are on the lot?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
86
There are 516 cars in a parking lot. One-third are blue, one-half are red, and the rest are black. How many black cars are on the lot?
train