Question 1009533
{{{60000=500p-p^2}}}

{{{p^2-500p+60000=0}}}

{{{p^2-500p+60000=0}}}...........factor

{{{p^2-300p-200p+60000=0}}}

{{{(p^2-300p)-(200p-60000)=0}}}

{{{p(p-300)-200(p-300)=0}}}

{{{(p-300)(p-200) = 0}}}

solutions:

{{{p=300}}} or {{{p=200}}}

so,  {{{p=200}}} is the fewest number of paintings the artist can sell to make a profit of at least ${{{60000}}}