Question 151027
if the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4. if the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9. find the original fraction.
:
Let "a certain fraction" = {{{n/d}}}
and
"if the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4."
{{{((n+6))/((d-5))}}} = {{{3/4}}}
and
"If the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9."
{{{d/n}}} - 1 = {{{16/9}}}
Add 1 to both sides:
{{{d/n}}} = {{{16/9}}} + {{{9/9}}}
{{{d/n}}} = {{{25/9}}}
That means:
n = 9
-- --- is the original fraction
d = 25
:
Using the 1st statment to check this:
{{{((9+6))/((25-5))}}} = {{{15/20}}} = {{{3/4}}}