fraction problems

Question

The denominator of a fraction is one more than twice the numerator. The value of the fractions is 6/7 if the numerator is increased by 5 and the denominator is decreased by 6. Find the fractions

Answer 1

the original fraction is

x

------------------

2x + 1

numerator is increased by 5 and the denominator is increased by 6:

x+5 6

-------------- = --------

2x - 5 7

Cross multiplies: 7(x+5) = 6(2x-5)

7x + 35 = 12x - 30

35 = 5x - 30

65 = 5x

x = 13

the original fraction : 13/27

(13+5)/(27-6) = 18/21 = 6/7

the old fraction is 13/27 and the new fraction is 6/7