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Algebra Level 2

The numerator of a fraction is 3 less than the denominator. If the numerator and denominator are each increased by 1, the value of the fraction is 3/4. Ex.( 2/3+2/3=4/6) meaning each number is individual. Find the numerator + denominator. Ex. 2/3=2+3=5


The answer is 19.

Robert Fritz by Robert Fritz , 20, USA

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4 solutions

Sulagna Debnath
Mar 21, 2014

Let X= Denominator X-3= numerator. hence, (x-3)/x=the fraction

according to the question, (x-3+1)/(x+1)=3/4 =>4x-8=3x=3 =>x=11 Hence, x-3=11-3=8 denominator+numerator =11+8 =19

2 Helpful 0 Interesting 0 Brilliant 0 Confused

x/(x+3) and (x+1)/(x+4)=3/4, so x = 8 so numerator is 8 and denominator is 11 and 8+11=19

Moshiur Mission - 7 years, 2 months ago
Anubhav Sharma
Apr 11, 2014

Let the numerator be n and denominator be d.

Then.

n/d

= (d - 3)/d

=> (d - 3) + 1/d + 1 = 3 / 4

=d - 2 / d + 1` = 3 / 4

By cross multiplication,

4(d - 2) = 3( d + 1)

4d - 8 = 3d + 3

4d - 3d = 8 + 3

d = 11

So, our denominator is 11. Since, numerator is 3 less than denominator.

n = d - 3

n= 11 - 3

n = 8

Hence, our fraction is 8/11

Finally ,the sum of numerator and denominator is 8 + 11 = 19

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Anurag Pandey
Mar 25, 2014

Let the numerator be x and the denominator , therefore, be x+3. When the numerator and denominator are both increased by 1 : x+1/x+3+1=x+1/x+4 According to the question : x+1/x+4= 3/4 => 4x+4=3x+12 => x = 8

Therefore , numerator + denominator = x + x + 3 = 16 + 3 = 19

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Let denominator be d.....then fraction=d-3/d...........(d-3+1)/(d+1)=3/4........solving=d=11.......fraction=8/11

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