Question 770243
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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/(x-2) = 2400/x + 100}}} dividing by 20 throughout,
{{{120/(x-2) = 120/x + 5}}}
Cross multiplying
{{{120*x = 120*(x - 2) + 5*x*(x - 2)}}}
{{{120*x = 120*x - 240 + 5*x^2 - 10*x}}}
{{{5*x^2 - 10*x - 240 = 0}}} Dividing by 5 throughout
{{{x^2 - 2*x - 48 = 0}}}
This is a standard quadratic equation which can be solved by factorizing.
{{{x^2 - 8*x + 6*x - 48 = 0}}}
{{{(x - 8)*(x + 6) = 0}}}
x = 8 or x = -6
Taking the positive value of x,
Number of fishermen = {{{highlight(8)}}}
Hope you got it :)
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