Question 143386
Let n=# of total students and c=cost per student (assuming they all go)




So if everyone goes, then the total cost $240 is divided equally among all n students. So the individual cost is


{{{c=240/n}}}




However, if 4 don't go, then simply subtract 4 from n to get {{{n-4}}}. Now divide 240 by {{{n-4}}} to get the individual cost plus $2



{{{240/(n-4)=c+2}}}




{{{240/(n-4)=240/n+2}}} Plug in {{{c=240/n}}}



{{{n*cross((n-4))(240/cross(n-4))=n(n-4)(240/cross(n)+2)}}} Multiply both sides by the LCD {{{n(n-4)}}}. This will clear the fractions



{{{240n=240(n-4)+2n(n-4)}}} Distribute



{{{240n=240n-960+2n^2-8n}}} Distribute again



{{{0=240n-960+2n^2-8n-240n}}}  Subtract 240n from both sides. 



{{{0=2n^2-8n-960}}} Combine like terms





{{{0=2(n-24)(n+20)}}} Factor the right side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{n-24=0}}} or  {{{n+20=0}}} 


{{{n=24}}} or  {{{n=-20}}}    Now solve for n in each case



So our possible answers are


 {{{n=24}}} or  {{{n=-20}}} 




However, since a negative number of students doesn't make any sense, this means that our only answer is {{{n=24}}} 




So there are a total of 24 students. Since 4 can't go, there are only 20 students who went to the computer center.