SOLUTION: Two thirds of a number added to the reciprocal of the number yields 25/6. What is the number?

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Question 680334: Two thirds of a number added to the reciprocal of the number yields 25/6. What is the number?
Answer by ReadingBoosters(3246) About Me  (Show Source):
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%282%2F3%29n+%2B+%281%2Fn%29+=+25%2F6
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Multiply the entire equation by 6n to be rid of fractions
6n%282%2F3%29n+%2B+6n%281%2Fn%29+=+6n%2825%2F6%29
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4n%5E2+%2B+6+=+25n
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4n%5E2+-+25n+%2B+6+=+0
(4n - 1)(n - 6) = 0
n = 6
n = 1/4
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The number can be highlight_green%286%29 or highlight_green%28%281%2F4%29%29
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Check
%282%2F3%29%286%29+%2B+%281%2F6%29 is 12%2F3+%2B+1%2F6+=+24%2F6+%2B+1%2F6+=+25%2F6 correct!
%282%2F3%29%281%2F4%29+%2B+4 is 2%2F12+%2B+4+=+2%2F12+%2B+48%2F12+=+50%2F12+=+25%2F6 correct!