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-2
So, 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.
