<human>:  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?
<bot>: Define a variable ** Let X be the price of a child ticket.
How much is an adult ticket? ** So the price of an adult ticket is X*2.
Write an equation ** We know from the problem that 400*X*2 + 200*X = 16,000.
Simplify ** After multiplying, we have 800*X+ 200*X = 16,000.
Simplify ** Combining like terms, we have 1000* X = 16,000.
Divide by 1000 ** Dividing both sides by 1000, we have X = $16.
How much is an adult ticket? ** The price of an adult ticket is $16 * 2 = $<<16*2=32>>32.
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