Question 1033107
Let the fraction be x/y.

The first part of the problem says that {{{(x-1)/y = 2/3}}}, while the second part says that {{{x/(y+5) = 1/2}}}.

The second equation is equivalent to {{{x = (1/2)(y+5)}}}.

Upon substitution into the first equation, we get {{{((1/2)(y+5)-1)/y = 2/3}}}

<==> {{{(1/2)y+5/2 - 1 = (2/3)y}}}

==> {{{y/2 +3/2 = (2/3)y}}}

==> {{{3/2 = (1/6)y}}}

==> y = 9.

==> x = 7.

==> the fraction is 7/9.