Question 114059
c = cost per student
n = number of students originally
{{{500 / n = c}}}
{{{500 / (n - 5) = c + 5}}}
substitute c in the 1st for c in the 2nd
{{{500/(n - 5) = (500 / n) + 5}}}
divide both sides by 5
{{{100/(n - 5) = (100 / n) + 1}}}
multiply both sides by {{{n(n - 5)}}}
{{{100n = 100(n - 5) + n(n - 5)}}}
{{{100n = 100n - 500 + n^2 - 5n}}}
subtract 100n from both sides
{{{n^2 - 5n - 500 = 0}}}
use the quadratic formula
a = 1
b = -5
c = -500
{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{n = (-(-5) +- sqrt( (-5)^2-4*1*(-500) ))/(2*1) }}}
{{{n = (5 +- sqrt(25 + 2000)) / 2}}}
{{{n = (5 +- sqrt(2025)) / 2}}}
{{{n = (5 +45) / 2}}}
{{{n = (5 - 45) / 2}}} ignore this answer, n can't be negative
{{{n = 50/2}}}
{{{n = 25}}}
{{{n - 5 = 20}}}
20 students attended, because 5 failed to come
check:
{{{500 / n = c}}}
{{{500 / (n - 5) = c + 5}}}
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{{{500/25 = c}}}
{{{20 = c}}} the cost would have been $20 per student if all had showed up
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{{{500 / (25 - 5) = 20 + 5}}}
{{{500 / 20 = 25}}} the cost was $25 per student when 5 didn't show up
{{{25 = 25}}}
OK