Question 214840
A class had lunch, and the bill totalled $239.25. 4 students had their birthday, therefore, they didn't need to pay. The other students had to pay $1 more than if all the students had paid. How many students had lunch? 
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n = total # of students
p = price of lunch per student
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p = 23925/n what they would have paid if all had contributed
p+100 = 23925/(n-4) what they had to pay without 4 chipping in
Sub for p into 2nd eqn
(23925/n) + 100 = 23925/(n-4)
Now it's just arithmetic
(23925 + 100n)/n = 23925/(n-4)
Cross multiply
(23925+100n)*(n-4) = 23925n
Divide by 25 (makes the numbers smaller)
(957+4n)(n-4) = 957n
4n^2 + 941n - 3828 = 957n
4n^2 - 16n - 3828 = 0
n^2 - 4n - 957 = 0
(n-33)*(n+29) = 0
n = -29 students (Ignore)
n = 33