The denominator of a fraction is 1 less than 5 times the numerator.

Question

If the numerator is increased by 5 and the denominator is decreased by 4, the resulting fraction is equal to ½. Find the ORIGINAL fraction.

Answer 1

d= 5n-1

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

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

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

n+5 = 5n/2 - 5/2

2n+10 = 5n -5

3n = 15

n= 5

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

d-4 = 2n+10 = 2(5)+10 = 20

d = 20+4 = 24

n =5, d= 24

(5+5).(24-4) = 10/20 = 1/2

Numerator = 5, Denominator = 24

Original fraction is 5/24