Question 127362
Frida's current age is x and Fredelyn's current age is y.


The first thing we know is that {{{x=y+5}}}


Three years from now Frida will be {{{x+3}}} and five years ago, Fredelyn was {{{y-5}}} and we know that the product of these two values is 90, so:


{{{(x+3)(y-5)=90}}}.


Substitute the expression for x in terms of y from the first equation into the second equation:
{{{((y+5)+3)(y-5)=90}}}


Simplify, expand, and put into standard form:
{{{(y+8)(y-5)=90}}}
{{{y^2+3y-40=90}}}
{{{y^2+3y-130=0}}}


{{{-130=(-10)(13)}}} and {{{3=-10+13}}}, so:


{{{(y-10)(y+13)=0}}}, hence Fredelyn is either 10 or -13 years old.  Since a negative number for the age of a person is absurd, exclude this root.  Fredelyn is therefore 10 years old.


From equation 1:  Frida is {{{10+5=15}}} years old.


Check:

{{{(15+3)(10-5)=18*5=90}}} answer checks.