<PRE><B>Question 832295</B>
Original sum of money, x for Jasmine and y for Luisa, the sum being {{{x+y}}}, which we do not yet know the values..  {{{x/y=4/5}}}


Luisa gives $9 to Jasmine.  Their monies are then x+9 and y-9.  These quantities are then given in the description as EQUAL.  This means {{{x+9=y-9}}}.


This situation has the symbolic description of :
{{{x/y=4/5}}} and {{{x+9=y-9}}}.
We may use the nine-dollar shift equation to solve for y, and substitute into the ratio equation, as you seem to have done.
{{{y=x+9+9}}}
{{{y=x+18}}}
-
Ratio {{{x/y=4/5}}}
{{{highlight(x/(x+18)=4/5)}}}, somewhat different from what you obtained.


Solve that one, {{{highlight(x/(x+18)=4/5)}}}, and you should find the correct values for x and y.   The original amounts for the parts of the sum of money which Jasmine and Luisa had.</PRE>