Calculator Mistake?

Number Theory Level 3

I bought four items from my local convenience store. The bill came to $7.11. I thought that amount must have been wrong, as I had seen the cashier multiplying the four prices together instead of adding them. (The cash register was broken, so he had to use a calculator instead.)

When I questioned the cashier about it, he agreed that he had multiplied the prices together, but said that in this case it didn't matter since the sum of the four items was also $7.11.

What was the price of the most expensive item (in dollars)?

Note: Each item costs a whole number of cents. For example, $2.11 is 211 cents, which is a whole number.


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