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
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.
1 answer
1 answer