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A man walks into 711 and buys four items, the items add up to 7.11 and multiply to 7.11. What are the prices for the 4 items?

During a talk about truth in mathematics, the presenter asked this question to the audience. I'm just curious as to what the answer is.

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    Hint: This is a Diophantine problem. Besides the sum and product, you also have that the answers (expressed in cents) are integers.2011-09-21
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    Wait, the man bought *numbers*? Where can I buy numbers? I call dibs on Euler-Mascheroni.2011-09-21
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    Hmmm, the prime factors of 711 are 3*3*79. There aren't many choices for the prices here, and none of them add up to 711. For example, 1*1*9*79 = 711, but the sum isn't even close.2011-09-21
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    @anon: if $\pi$ is too expensive, maybe I can just buy a piece?2011-09-21
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    @DeepYellow: $$\frac{abcd}{100^4}=\frac{711}{100}$$ $$\implies abcd=2^6 3^2 5^6 79$$2011-09-21
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    @anon: Right you are! (duh!)2011-09-21

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