Question 196173
Let {{{s}}}= the number of students who
participated in the picnic.
The expense of 3600 was based on {{{s + 15}}}
students participating
The cost per student would have been {{{3600/(s + 15)}}}
But now the cost per student is {{{3600/s}}}
The difference between these costs is {{{8}}}
{{{3600/s - 3600/(s + 15) = 8}}}
Multiply both sides by {{{s*(s + 15)}}}
{{{3600*(s + 15) - 3600s = 8*s*(s + 15)}}}
{{{3600s + 54000 - 3600s = 8s^2 + 120s}}}
{{{54000 = 8s^2 + 120s}}}
{{{s^2 + 15s = 6750}}}
Complete the square:
{{{s^2 + 15s + (15/2)^2 = 6750 + (15/2)^2}}}
{{{(s + 15/2)^2 = 27000/4 + 225/4}}}
{{{(s + 15/2)^2 = 27225/4}}}
Take the square root of both sides
{{{s + 15/2 = 165/2}}}
{{{s = (165 - 15)/2}}}
{{{s = 75}}}
75 students participated in the picnic
check answer:
{{{3600/s - 3600/(s + 15) = 8}}}
{{{3600/75 - 3600/(75 + 15) = 8}}}
{{{48 - 40 = 8}}}
{{{8 = 8}}}
OK