Mathematics: Aparty 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?

Aparty of fishermen rented a boat for $240. two

korban23

31.12.2021

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 = $\frac{240}{x}$

New number of fisherman in the party = x-2

So, new average cost per person = $\frac{240}{x-2}$

As 2 persons withdrew, the cost increased by $10 for others.

So, equation becomes:

$\frac{240}{x-2}-\frac{240}{x}=10$

=> 240x-240(x-2)= 10x(x-2)

Solving this we get the quadratic equation:

$10x^{2}-20x-480=0$

Factoring out 10 common;

$x^{2}-2x-48=0$

=> $x^{2}-8x+6x-48=0$

=> x(x-8)+6(x-8)=0

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.

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