SOLUTION: Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member i

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Question 114059: Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
c = cost per student
n = number of students originally
500+%2F+n+=+c
500+%2F+%28n+-+5%29+=+c+%2B+5
substitute c in the 1st for c in the 2nd
500%2F%28n+-+5%29+=+%28500+%2F+n%29+%2B+5
divide both sides by 5
100%2F%28n+-+5%29+=+%28100+%2F+n%29+%2B+1
multiply both sides by n%28n+-+5%29
100n+=+100%28n+-+5%29+%2B+n%28n+-+5%29
100n+=+100n+-+500+%2B+n%5E2+-+5n
subtract 100n from both sides
n%5E2+-+5n+-+500+=+0
use the quadratic formula
a = 1
b = -5
c = -500
n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
n+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A%28-500%29+%29%29%2F%282%2A1%29+
n+=+%285+%2B-+sqrt%2825+%2B+2000%29%29+%2F+2
n+=+%285+%2B-+sqrt%282025%29%29+%2F+2
n+=+%285+%2B45%29+%2F+2
n+=+%285+-+45%29+%2F+2 ignore this answer, n can't be negative
n+=+50%2F2
n+=+25
n+-+5+=+20
20 students attended, because 5 failed to come
check:
500+%2F+n+=+c
500+%2F+%28n+-+5%29+=+c+%2B+5
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500%2F25+=+c
20+=+c the cost would have been $20 per student if all had showed up
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500+%2F+%2825+-+5%29+=+20+%2B+5
500+%2F+20+=+25 the cost was $25 per student when 5 didn't show up
25+=+25
OK