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? Let's answer step by step:
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 = $32. The answer: 32.