Question 180262
Let {{{n}}} = the number of people chartered originally
given:
{{{34848/n}}} = cost per person originally
{{{34848/n + 24}}} = cost per person after 11 people cancel
{{{34848/(n - 11) = 34848/n + 24}}}
Multiply both sides by {{{n*(n - 11)}}}
{{{34848n  = 34848*(n - 11) + 24*n*(n - 11)}}}
{{{34848n  = 34848n - 383328 + 24n^2 - 264n)}}}
{{{24n^2 - 264n - 383328 = 0}}}
{{{n^2 - 11n - 15972 = 0}}}
 {{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = -11}}}
{{{c = -15972}}}
{{{n = (-(-11) +- sqrt( (-11)^2-4*1*(-15972) ))/(2*1) }}}
{{{n = (11 +- sqrt(121 + 63888 )) / 2 }}}
{{{n = (11 +- sqrt(64009 )) / 2 }}}
{{{n = (11 +- 253) / 2 }}}
{{{n = 132}}}
The other solution for {{{x}}} is negative & can't be used
132 people originally intended to take the trip
check answer:
{{{34848/(n - 11) = 34848/n + 24}}}
{{{34848/(132 - 11) = 34848/132 + 24}}}
{{{34848/121 = 34848/132 + 24}}}
{{{288 = 264 + 24}}}
{{{288 = 288}}}
OK