SOLUTION: A group of fishermen rented a boat for Php2400.00. Two of the men withdrew from the party and as a result, the share of each of those remaining was increased by 100. How many were

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Question 770243: A group of fishermen rented a boat for Php2400.00. Two of the men withdrew from the party and as a result, the share of each of those remaining was increased by 100. How many were in the original group? Thank you! :)
Answer by ramkikk66(644) About Me  (Show Source):
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A group of fishermen rented a boat for Php2400.00. Two of the men withdrew from the party and as a result, the share of each of those remaining was increased by 100. How many were in the original group? Thank you! :) 
Ans:
Let the original number of people be x.
Then share of each person = 2400/x
After 2 people withdraw, the new number of people = (x - 2)
New share for each = 2400/(x - 2)
This new share is 100 more than the original.
So we get the equation
2400%2F%28x-2%29+=+2400%2Fx+%2B+100 dividing by 20 throughout,
120%2F%28x-2%29+=+120%2Fx+%2B+5
Cross multiplying
120%2Ax+=+120%2A%28x+-+2%29+%2B+5%2Ax%2A%28x+-+2%29
120%2Ax+=+120%2Ax+-+240+%2B+5%2Ax%5E2+-+10%2Ax
5%2Ax%5E2+-+10%2Ax+-+240+=+0 Dividing by 5 throughout
x%5E2+-+2%2Ax+-+48+=+0
This is a standard quadratic equation which can be solved by factorizing.
x%5E2+-+8%2Ax+%2B+6%2Ax+-+48+=+0
%28x+-+8%29%2A%28x+%2B+6%29+=+0
x = 8 or x = -6
Taking the positive value of x,
Number of fishermen = highlight%288%29
Hope you got it :)