PROBLEM: 7-11

A guy walks into a 7-11 store and selects four items to buy. The clerk at the counter informs the gentleman that the total cost of the four items is $7.11. He was completely surprised that the cost was the same as the name of the store. The clerk informed the man that he simply multiplied the cost of each item and arrived at the total. The customer calmly informed the clerk that the items should be added and not multiplied. The clerk then added the items together and informed the customer that the total was still exactly $7.11.

What are the exact (not rounded to the nearest cent) costs of each item?

I started working on this problem and thought I was progressing quite well but I seemed to exhaust all possibilities. I put the problem aside for a few weeks but kept thinking about the problem. When I finally returned to the problem, I noticed that I had read the problem wrong and instead of using 4 items to add-up to and multiple together to give me $7.11, I was only using 2 items. I have only started to rethink how I am going to approach this problem. This problem interests me because whenever I am in a store I am always trying to figure out how much things will cost.

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