Question 507794
Let the number of people be n.
{{{300/n = n-5}}} "...the number of hectares per person ({{{300/n}}}) was 5 less than the number of persons (n-5)." Multiply both sides by n.
{{{300 = n^2-5n}}} Subtract 300 from both sides and rearrange as:
{{{n^2-5n-300 = 0}}} Solve by factoring.
{{{(n+15)(n-20) = 0}}} Apply the zero product rule.
{{{n+15 = 0}}} or {{{n-20 = 0}}} so that...
{{{n = -15}}} or {{{n = 20}}} Discard the negative solution as number of people can't be negative.
The number of people is 20.
Check:
{{{300/20 = 20-5}}}
{{{15 = 15}}} OK