SOLUTION: the denominator of a fraction is 3 more than the numerator. if both numerator and denominator are increased by 1, the resulting fractions is 3/4 find the fraction?
Question 1197215: the denominator of a fraction is 3 more than the numerator. if both numerator and denominator are increased by 1, the resulting fractions is 3/4 find the fraction? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website! .
The fraction is , and the equation to find "n" is
= .
Cross-multiply, simplify and find "n"
4*(n+1) = 3*((n+3)+1),
4n + 4 = 3*(n+4)
4n + 4 = 3n + 12
4n - 3n = 12 - 4
n = 8
ANSWER. The fraction is .
Probably a formal algebraic solution, as shown by the other tutor, was what you wanted....
However, this kind of problem can be solved easily using logical reasoning and simple arithmetic.
The denominator of the fraction is 3 more than the numerator; when both numerator and denominator are increased by 1, the denominator is still 3 more than the numerator.
The requirement is that the resulting fraction (simplified) is 3/4. The task then is to write a fraction equivalent to 3/4 in which the denominator is 3 more than the numerator.
In the fraction 3/4, the denominator is only 1 more than the numerator, so multiply numerator and denominator by 3 to get an equivalent fraction in which the denominator is 3 more than the numerator.
So the resulting fraction, after adding 1 to numerator and denominator of the original fraction, is 9/12; and that means the original fraction was 8/11.