SOLUTION: A civic club charters a bus for one day at a cost of $575. When two more people join the group, each person's cost decreases by $2. How many people were in the original group?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A civic club charters a bus for one day at a cost of $575. When two more people join the group, each person's cost decreases by $2. How many people were in the original group?       Log On


   

Question 944261: A civic club charters a bus for one day at a cost of $575. When two more people join the group, each person's cost decreases by $2. How many people were in the original group?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the original number of people
in the group
+n+%2B+2+ = The number when 2 people
join the group
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+575%2Fn+ = original cost/person
given:
+575%2F%28+n+%2B+2+%29+=+575%2Fn+-+2+
Multiply both sides by +n%2A%28+n%2B2+%29+
+575n+=+575%2A%28+n%2B2+%29+-+2n%2A%28+n%2B2+%29+
+575n+=+575n+%2B+1150+-+2n%5E2+-+4n+
+2n%5E2+%2B+4n+-+1150+=+0+
+n%5E2+%2B+2n+-+575+=+0+
Use the quadratic formula
+n+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+2+
+c+=+-575+
+n+=+%28+-2+%2B-+sqrt%28+2%5E2+-+4%2A1%2A%28-575%29+%29%29+%2F+%282%2A1%29+
+n+=+%28+-2+%2B-+sqrt%28+4+%2B+2300+%29%29+%2F+2+
+n+=+%28+-2+%2B-+sqrt%28+2304+%29%29+%2F+2+
+n+=+%28+-2+%2B+47.96+%29+%2F+2+
+n+=+45.96%2F2+
+n+=+22.98+
23 people were in the original group
check:
+575%2F24.98+=+575%2F22.98+-+2+
+23.02+=+25.02+-+2+
+23.02+=+23.02+
OK
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Normally +n+ would be a whole number, so
I don't know what happened. I think my equation
is OK, so check my math