Question 255012
 The bill came to $239.25. Four students had birthdays that day, and it was agreed that these four should not have to pay for lunch.
 The other students had to pay $1 more than if all students had paid. How many students had lunch?
:
Let x = no. of students that had lunch
then
(x-4) = no. that actually paid
:
{{{239.25/x}}} = cost per student if all paid
{{{239.25/((x-4)))}}} = cost if 4 did not pay
:
The equation
:
{{{239.25/((x-4))}}} - {{{239.25/x}}}= $1
:
Multiply by x(x-4), results:
239.25x - 239.25(x-4) = x(x-4)
:
239.25x - 239.25x + 957 = x^2 - 4x
:
a quadratic equation from this
x^2 - 4x - 957 = 0
:
Factors to 
(x-33)(x+29) = 0
:
positive solution
x = 33 students had lunch 
and
29 students paid; 239.25/29 = $8.25 as you found