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
In recent years, the awareness of traffic safety among citizens has gradually increased, leading to a greater demand for helmets. A certain store purchased two types of helmets, type A and type B. It is known that they bought 20 type A helmets and 30 type B helmets, spending a total of 2920 yuan. The unit price of type A helmets is 11 yuan higher than the unit price of type B helmets.  
$(1)$ What are the unit prices of type A and type B helmets, respectively?  
$(2)$ The store decides to purchase 40 more helmets of type A and type B. They coincide with a promotional event by the manufacturer: type A helmets are sold at 20% off the unit price, and type B helmets are discounted by 6 yuan each. If the number of type A helmets purchased this time is not less than half the number of type B helmets, how many type A helmets should be purchased to minimize the total cost of this purchase? What is the minimum cost?
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1976
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In recent years, the awareness of traffic safety among citizens has gradually increased, leading to a greater demand for helmets. A certain store purchased two types of helmets, type A and type B. It is known that they bought 20 type A helmets and 30 type B helmets, spending a total of 2920 yuan. The unit price of type A helmets is 11 yuan higher than the unit price of type B helmets.  
$(1)$ What are the unit prices of type A and type B helmets, respectively?  
$(2)$ The store decides to purchase 40 more helmets of type A and type B. They coincide with a promotional event by the manufacturer: type A helmets are sold at 20% off the unit price, and type B helmets are discounted by 6 yuan each. If the number of type A helmets purchased this time is not less than half the number of type B helmets, how many type A helmets should be purchased to minimize the total cost of this purchase? What is the minimum cost?
train