SOLUTION: The student council of Sta. Lucia High School needed 2,500.00 for an annual trip. If five more members joined the group, each members would then save 5.00. How many students planne

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Question 477400: The student council of Sta. Lucia High School needed 2,500.00 for an annual trip. If five more members joined the group, each members would then save 5.00. How many students planned to make the trip?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = number of students who planned to take the trip
given:
the cost per student is +2500+%2F+x+
If 5 more joined the group, the cost per student would be
+2500%2Fx+-+5+
----------------
I can write the equation:
+2500+%2F+x+-+5=+2500%2F%28x+%2B+5%29++
Multiply both sides by +x%2A%28x%2B5%29+
+2500%2A%28x%2B5%29+-+5x%2A%28x%2B5%29+=+2500x+
+2500x+%2B+12500+-+5x%5E2+-+25x+=+2500x%0D%0A%7B%7B%7B+5x%5E2+%2B+25x+-+12500+=+0+
++x%5E2+%2B+5x+-+2500+=+0+
Using quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+5+
+c+=+-2500+
x+=+%28-5+%2B-+sqrt%28+5%5E2+-+4%2A1%2A%28-2500%29+%29%29%2F%282%2A1%29+
x+=+%28-5+%2B-+sqrt%28+25+%2B+10000+%29%29+%2F+2+
x+=+%28-5+%2B-+sqrt%28+10025+%29%29+%2F+2+
+x+=+%28+-+5+%2B+100.125+%29+%2F+2+
+x+=+95.125%2F2+
+x+=+47.56+
I can round this to 48 students planned to take the trip
check answer:
+2500+%2F+%2848%2B5%29+=+2500%2F48+-+5+
+2500%2F53+=+2500%2F48+-+5+
+47.17+=+52.08+-+5+
+47.17+=+47.08+
This seems close enough
Hope I got it right