Question 626840
Let {{{x}}} be the total number of butterflies in the garden.
{{{(1/5)x}}} butterflies are on jasmines.
{{{(1/3)x}}} butterflies (a larger number) are on roses.
The difference is
{{{(1/3)x-(1/5)x=(1/3-1/5)x=(5/15-3/15)x=(2/15)x}}}
Three times that difference,
{{{3*(2/15)x=(2/5)x}}} ,
is the number of butterflies on lilies.
The total number is
{{{x=(1/3)x+(1/5)x+(2/5)x+1}}} --> {{{x=(1/3+1/5+2/5)x+1}}} --> {{{x=(5/15+3/15+6/15)x+1}}} --> {{{x=(14/15)x+1}}} 
Multiplying both sides of the equal sign times 15:
{{{15x=15((14/15)x+1)}}} --> {{{15x=14x+15}}}
Subtracting 14x from both sides of the equal sign:
{{{15x=14x+15}}} --> {{{15x-14x=14x+15-14x}}} -->  {{{highlight(x=15)}}}