SOLUTION: The reciprocal of a number plus the reciprocal of three times the number equals (1)/(3) Find the number.

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Question 482694: The reciprocal of a number plus the reciprocal of three times the number equals (1)/(3)
Find the number.
Found 2 solutions by jainpreeja, MathTherapy:
Answer by jainpreeja(10) About Me  (Show Source):
You can put this solution on YOUR website!
he reciprocal of a number plus the reciprocal of three times the number equals (1)/(3)
Find the number.
we take x is that number.
1/x+ 3/x=1/3
1+3/x=1/3 (taking LCM)
4/x=1/3
x=12 (cross multiplication)

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!


Let the number be N
Then its reciprocal is 1%2FN
Three (3) times the number would be 3N
The reciprocal of 3 times the number would be 1%2F3N

Since the sum of the reciprocal of the number and the reciprocal of 3 times the number is 1%2F3, then we have:
1%2FN+%2B+1%2F3N+=+1%2F3

Multiplying by LCD, 3N gives us: 3 + 1 = N -------- N, or the number is highlight_green%284%29

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Check
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1%2F4+%2B+1%2F%283%2A4%29+=+1%2F3
1%2F4+%2B+1%2F12+=+1%2F3
3%2F12+%2B+1%2F12+=+4%2F12
4%2F12+=+4%2F12
1%2F3+=+1%2F3

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