SOLUTION: In an unknown fraction the denominator is one more than twice the numerator.When 2 (1/10) is added to this fraction,the result is equal to the reciprocal of the unknown fraction.fi
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Question 866131: In an unknown fraction the denominator is one more than twice the numerator.When 2 (1/10) is added to this fraction,the result is equal to the reciprocal of the unknown fraction.find the unkown fraction.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
In an unknown fraction the denominator is one more than twice the numerator.
When 2 (1/10) is added to this fraction,the result is equal to the reciprocal of the unknown fraction.
find the unknown fraction.
:
Let x = the numerator of the unknown fraction
then "the denominator is one more than twice the numerator", therefore:
(2x+1) = the denominator
:
Change 2 to
:
"When 2 (1/10) is added to this fraction,the result is equal to the reciprocal of the unknown fraction."
+ =
mult equation by 10x(2x+1), cancel the denominators and you have
10x(x) + 21x(2x+1) = 10(2x+1)(2x+1)
10x^2 + 42x^2 + 21x = 10(4x^2 + 4x + 1)
52x^2 + 21x = 40x^2 + 40x + 10
combine like terms on the left
52x^2 - 40x^2 + 21x - 40x - 10 = 0
12x^2 - 19x - 10 = 0
Factors to
(12x + 5)(x - 2) = 0
only the positive integer makes sense here
x = 2
then the unknown fraction:
=
:
:\
Check this
+ =
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