SOLUTION: Certain number of students planed to go for a picnic. Tht total expense was estimated to be Rs.3600-. But 15 students could not go. Each student participated had to pay Rs.8/- more

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Certain number of students planed to go for a picnic. Tht total expense was estimated to be Rs.3600-. But 15 students could not go. Each student participated had to pay Rs.8/- more      Log On


   

Question 196173: Certain number of students planed to go for a picnic. Tht total expense was estimated to be Rs.3600-. But 15 students could not go. Each student participated had to pay Rs.8/- more. Then howmany students participated in the picnic
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s= the number of students who
participated in the picnic.
The expense of 3600 was based on s+%2B+15
students participating
The cost per student would have been 3600%2F%28s+%2B+15%29
But now the cost per student is 3600%2Fs
The difference between these costs is 8
3600%2Fs+-+3600%2F%28s+%2B+15%29+=+8
Multiply both sides by s%2A%28s+%2B+15%29
3600%2A%28s+%2B+15%29+-+3600s+=+8%2As%2A%28s+%2B+15%29
3600s+%2B+54000+-+3600s+=+8s%5E2+%2B+120s
54000+=+8s%5E2+%2B+120s
s%5E2+%2B+15s+=+6750
Complete the square:
s%5E2+%2B+15s+%2B+%2815%2F2%29%5E2+=+6750+%2B+%2815%2F2%29%5E2
%28s+%2B+15%2F2%29%5E2+=+27000%2F4+%2B+225%2F4
%28s+%2B+15%2F2%29%5E2+=+27225%2F4
Take the square root of both sides
s+%2B+15%2F2+=+165%2F2
s+=+%28165+-+15%29%2F2
s+=+75
75 students participated in the picnic
check answer:
3600%2Fs+-+3600%2F%28s+%2B+15%29+=+8
3600%2F75+-+3600%2F%2875+%2B+15%29+=+8
48+-+40+=+8
8+=+8
OK