SOLUTION: The denominator of a proper fraction is 1 less than twice the numerator. The difference between the digits of the numerator and denominator is 3. Find the fraction and its reciproc

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The denominator of a proper fraction is 1 less than twice the numerator. The difference between the digits of the numerator and denominator is 3. Find the fraction and its reciproc      Log On


   

Question 698838: The denominator of a proper fraction is 1 less than twice the numerator. The difference between the digits of the numerator and denominator is 3. Find the fraction and its reciprocal.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The denominator of a proper fraction is 1 less than twice the numerator.
The difference between the digits of the numerator and denominator is 3.
Find the fraction and its reciprocal.
:
Since it is a proper fraction we know that d > n
An equation for each statement
:
d = 2n - 1
and
d - n = 3
d = (n+3)
Replace d in the 1st equation
n + 3 = 2n - 1
3 + 1 = 2n - n
n = 4
then
d = 4 + 3
d = 7
:
4%2F7 is the fraction and the reciprocal: 7%2F4