Question

If denominator of a fraction is one less than twice its numerator.If 3 is
added to the numerator and 4 is added to the deominator,the fraction beomes
3/5.Find the fraction.

Answer 1

f = fraction

n = numerator

d = denominator

f = n / d

Denominator of a fraction is one less than twice its numerator means

d = 2 n - 1

If 3 is added to the numerator and 4 is added to the deominator,the fraction becomes 3 / 5 means:

( n + 3 ) / ( d + 4 ) = 3 / 5

Replace d with 2 n - 1 in this equation.

( n + 3 ) / ( 2 n - 1 + 4 ) = 3 / 5


( n + 3 ) / ( 2 n + 3 ) = 3 / 5

Cross multiply

5 ( n + 3 ) = 3 ( 2 n + 3 )

5 n + 15 = 6 n + 9

Subtract 5 n to both sides

15 = n + 9

Subtract 9 n to both sides

6 = n

n = 6


d = 2 n - 1

d = 2 ∙ 6 - 1

d = 12 - 1

d = 11


f = n / d = 6 / 11


Check result:

( n + 3 ) / ( d + 4 ) = 3 / 5

( 6 + 3 ) / ( 11 + 4 ) = 3 / 5

9 / 15 = 3 / 5

3 ∙ 3 / 3 ∙ 5 = 3 ∙ 5