Question

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 1

In the original party, there were 8 fishermen.

Explanation:

A party of fishermen rented a boat for $240.

Let original number of fisherman in party be x.

So, average cost per person =
`(240)/(x)`

New number of fisherman in the party = x-2

So, new average cost per person =
`(240)/(x-2)`

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

So, equation becomes:

`(240)/(x-2)-(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.