SOLUTION: I'm not sure if I'm understanding this word problem correctly, could I have some help, thanks. The reciprocal of two more than a number is three fourths of the reciprocal of the nu

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Question 130067: I'm not sure if I'm understanding this word problem correctly, could I have some help, thanks. The reciprocal of two more than a number is three fourths of the reciprocal of the number itself. what is the number? I have the expression x+2x=3/4 answer x=1/4 Is this correct? Please let me know, if not could you help me understand it, thank you.
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Let n be the required number.
"The reciprocal of 2 more than a number..." can be expressed as:
1%2F%28n%2B2%29
"...three fourths of the reciprocal of the number itself." can be expressed as:
%283%2F4%29%281%2Fn%29
Setting these two equal to each other we get:
1%2F%28n%2B2%29+=+%283%2F4%29%281%2Fn%29 Simplify.
1%2F%28n%2B2%29+=+3%2F4n Cross-multiply by the denominators.
4n+=+3%28n%2B2%29 Simplify.
4n+=+3n+%2B+6 Subtract 3n from both sides.
n+=+6
The number is 6.
Check:
1%2F%28n%2B2%29+=+%283%2F4%29%281%2Fn%29 Substitute n = 6.
1%2F%28n%2B2%29+=+%283%2F4%29%281%2F6%29
1%2F8+=+3%2F24
1%2F8+=+1%2F8 It checks!