A party of fishermen rented a boat for $240. Two of the fishermen had to withdraw from the party and, as a result, the share of each of the others was increased by $10. How many were in the original party?

Answer:In the original party, there were 8 fishermen.Step-by-step explanation:A party of fishermen rented a boat for $240.Let original number of fisherman in party be x.So, average cost per person = [tex]\frac{240}{x}[/tex]New number of fisherman in the party = x-2So, new average cost per person = [tex]\frac{240}{x-2}[/tex]As 2 persons withdrew, the cost increased by $10 for others.So, equation becomes:[tex]\frac{240}{x-2}-\frac{240}{x}=10[/tex]=> [tex]240x-240(x-2)= 10x(x-2)[/tex]Solving this we get the quadratic equation:[tex]10x^{2}-20x-480=0[/tex]Factoring out 10 common;[tex]x^{2}-2x-48=0[/tex]=> [tex]x^{2}-8x+6x-48=0[/tex]=>  [tex]x(x-8)+6(x-8)=0[/tex]We get the roots as (x-8) and (x+6)So, x = 8 and x = -6(neglecting negative value)Hence, there were 8 fisherman in the original party.