x<y<z (x,y,z∊N) 1/x+1/y+1/z=1, x+y+z=?

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I solved it like this: since 1/2 + 1/3 + 1/4 i calculated to be too big by .033, i made the last one slightly smaller to have 1/2 + 1/3 + 1/5, which i calculated to equal 1. Then I added those denominators to get 10.

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