document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #488384 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+x+\"$ = the number staying overnight
\n" ); document.write( " $\"+4800+%2F+x+\"$ = the bill for each person
\n" ); document.write( "-------------
\n" ); document.write( " $\"+4800+=+%28+4800%2F%28+x%2B4+%29+%2B+200+%29%2Ax+\"$
\n" ); document.write( "( total bill ) = ( same bill divided among ( x+4 ) people + add the savings back in for each person )
\n" ); document.write( "times ( original number of people )
\n" ); document.write( "-------------------------------
\n" ); document.write( " $\"+4800+=+4800x+%2F+%28+x+%2B+4+%29+%2B+200x+\"$
\n" ); document.write( " $\"+4800%2A%28+x%2B4+%29++=+4800x+%2B+200x%2A%28+x%2B4+%29+\"$
\n" ); document.write( " $\"+4800x+%2B+19200+=+4800x+%2B+200x%5E2+%2B+800x+\"$
\n" ); document.write( " $\"+200x%5E2+%2B+800x+-+19200+=+0+\"$
\n" ); document.write( " $\"+x%5E2+%2B+4x+-+96+=+0+\"$
\n" ); document.write( " $\"+%28+x+%2B+12+%29%2A%28+x+-+8+%29+\"$ ( by inspection )
\n" ); document.write( " $\"+x+=+8+\"$
\n" ); document.write( "------------
\n" ); document.write( "There are 8 people staying overnight
\n" ); document.write( "check:
\n" ); document.write( " $\"+4800%2F8+=+600+\"$ per person
\n" ); document.write( "With 4 more people:
\n" ); document.write( " $\"+%28+600+-+200+%29%2A12+=+4800+\"$
\n" ); document.write( "OK\r
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