SOLUTION: The social club charters a plane at a cost of $34848 to take a group of people to Atlanta. At the last minute 11 people from the group decide not to go. This raises the transportat

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Question 180262: The social club charters a plane at a cost of $34848 to take a group of people to Atlanta. At the last minute 11 people from the group decide not to go. This raises the transportation cost per person by $24. How many people were originally intended to take the trip?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the number of people chartered originally
given:
34848%2Fn = cost per person originally
34848%2Fn+%2B+24 = cost per person after 11 people cancel
34848%2F%28n+-+11%29+=+34848%2Fn+%2B+24
Multiply both sides by n%2A%28n+-+11%29
34848n++=+34848%2A%28n+-+11%29+%2B+24%2An%2A%28n+-+11%29
34848n++=+34848n+-+383328+%2B+24n%5E2+-+264n%29
24n%5E2+-+264n+-+383328+=+0
n%5E2+-+11n+-+15972+=+0
n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+-11
c+=+-15972
n+=+%28-%28-11%29+%2B-+sqrt%28+%28-11%29%5E2-4%2A1%2A%28-15972%29+%29%29%2F%282%2A1%29+
n+=+%2811+%2B-+sqrt%28121+%2B+63888+%29%29+%2F+2+
n+=+%2811+%2B-+sqrt%2864009+%29%29+%2F+2+
n+=+%2811+%2B-+253%29+%2F+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%2F%28n+-+11%29+=+34848%2Fn+%2B+24
34848%2F%28132+-+11%29+=+34848%2F132+%2B+24
34848%2F121+=+34848%2F132+%2B+24
288+=+264+%2B+24
288+=+288
OK