Let X be the price of a child ticket.

So the price of an adult ticket is X*2.

We know from the problem that 400*X*2 + 200*X = 16,000.

After multiplying, we have 800*X+ 200*X = 16,000.

Combining like terms, we have 1000* X = 16,000.

Dividing both sides by 1000, we have X = $16.

The price of an adult ticket is $16 * 2 = $<<16*2=32>>32.

# Answer

32
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
400 adults and 200 children go to a Broadway show. The price of an adult ticket is twice that of a child's ticket. What is the price of an adult ticket if the total amount collected is $16,000?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
32
400 adults and 200 children go to a Broadway show. The price of an adult ticket is twice that of a child's ticket. What is the price of an adult ticket if the total amount collected is $16,000?
train