SOLUTION: The hotel bill for a number of people for overnight stay is Rs4800. If there were four people more, the bill each person had to pay would have reduced by Rs200. Find the number of

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Question 810752: The hotel bill for a number of people for overnight stay is Rs4800. If there were four people more, the bill each person had to pay would have reduced by Rs200. Find the number of people staying overnight.
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
There is something wrong with your problem.
Why would the bill be reduced if there are more people?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the number staying overnight
+4800+%2F+x+ = the bill for each person
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+4800+=+%28+4800%2F%28+x%2B4+%29+%2B+200+%29%2Ax+
( total bill ) = ( same bill divided among ( x+4 ) people + add the savings back in for each person )
times ( original number of people )
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+4800+=+4800x+%2F+%28+x+%2B+4+%29+%2B+200x+
+4800%2A%28+x%2B4+%29++=+4800x+%2B+200x%2A%28+x%2B4+%29+
+4800x+%2B+19200+=+4800x+%2B+200x%5E2+%2B+800x+
+200x%5E2+%2B+800x+-+19200+=+0+
+x%5E2+%2B+4x+-+96+=+0+
+%28+x+%2B+12+%29%2A%28+x+-+8+%29+ ( by inspection )
+x+=+8+
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There are 8 people staying overnight
check:
+4800%2F8+=+600+ per person
With 4 more people:
+%28+600+-+200+%29%2A12+=+4800+
OK