Give the step-by-step reasoning process and then the final answer. Mr. and Mrs. Boyden take their 3 children to a leisure park. They buy tickets for the whole family. The cost of an adult ticket is $6 more than the cost of a child ticket. The total cost of the 5 tickets is $77. What is the cost of an adult ticket?
Let X be the cost of an adult ticket. So the cost of a child ticket is X - 6. The total cost of the 5 tickets is X * 2 + 3 * (X - 6) = 77. X * 2 + 3 * X - 3 * 6 = 77. 5 * X - 18 = 77. 5 * X = 77 + 18 = 95. X = 19.
The final answer: 19.