You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
The principal of a school plans to lead the city-level "Outstanding Students" to Beijing for a trip during the summer vacation. Travel Agency A says, "If the principal buys a full-price ticket, the rest of the students can enjoy a half-price discount." Travel Agency B says, "Including the principal, everyone will enjoy a 40% discount off the full ticket price (i.e., charged at 60% of the full ticket price)." If the full ticket price is 240 yuan.  
(Ⅰ) Let the number of students be $x$, the charge by Travel Agency A be $y_{\text{甲}}$, and the charge by Travel Agency B be $y_{\text{乙}}$, calculate the charges by the two travel agencies respectively (establish the expressions);  
(Ⅱ) When the number of students is what, the charges by the two travel agencies are the same;  
(Ⅲ) Discuss which travel agency is more cost-effective based on the number of students $x$.
user
4
rule
The principal of a school plans to lead the city-level "Outstanding Students" to Beijing for a trip during the summer vacation. Travel Agency A says, "If the principal buys a full-price ticket, the rest of the students can enjoy a half-price discount." Travel Agency B says, "Including the principal, everyone will enjoy a 40% discount off the full ticket price (i.e., charged at 60% of the full ticket price)." If the full ticket price is 240 yuan.  
(Ⅰ) Let the number of students be $x$, the charge by Travel Agency A be $y_{\text{甲}}$, and the charge by Travel Agency B be $y_{\text{乙}}$, calculate the charges by the two travel agencies respectively (establish the expressions);  
(Ⅱ) When the number of students is what, the charges by the two travel agencies are the same;  
(Ⅲ) Discuss which travel agency is more cost-effective based on the number of students $x$.
train