Question 1051038
Originally,
1.{{{P[1]*K=540}}}
then,
2.{{{(P[1]-2)*(K+3)=540}}}
From eq. 1,
{{{P[1]=540/K}}}
Substituting,
{{{(540/K-2)(K+3)=540}}}
{{{540+1620/K-2K-6=540}}}
{{{1620/K-2K-6=0}}}
{{{-2K^2-6K+1620=0}}}
{{{K^2+3K-810=0}}}
{{{(K+30)(K-27)=0}}}
K must be positive, so only one solution works,
{{{K-27=0}}}
{{{K=27}}}
So then,
{{{P[1]=540/27}}}
{{{P[1]=20}}}
She originally bought 27 kilos at $20/kilo.