document.write( "Question 992363: A college charters a bus for $1900 to take a group of students to see a Broadway production. When 2 more students join the trip, the cost per student decreases by $2.50. How many students were in the original group? \n" ); document.write( "

Algebra.Com's Answer #612035 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+x+\"$ = the original number of students
\n" ); document.write( " $\"+1900%2Fx+-+2.5+=+1900%2F%28+x+%2B+2+%29+\"$
\n" ); document.write( "Multiply both sides by $\"+x%2A%28+x%2B2+%29+\"$
\n" ); document.write( " $\"+1900%2A%28+x%2B2+%29+-+2.5%2Ax%2A%28+x%2B2+%29+=+1900x+\"$
\n" ); document.write( " $\"+1900x+%2B+3800+-+2.5x%5E2+-+5x+=+1900x+\"$
\n" ); document.write( " $\"+2.5x%5E2+%2B+5x+-+3800+=+0+\"$
\n" ); document.write( " $\"+25x%5E2+%2B+50x+-+38000+=+0+\"$
\n" ); document.write( " $\"+x%5E2+%2B+2x+=+1520+\"$
\n" ); document.write( "Complete the square
\n" ); document.write( " $\"+x%5E2+%2B+2x+%2B+%282%2F2%29%5E2+=+1520+%2B+%282%2F2%29%5E2+\"$
\n" ); document.write( " $\"+x%5E2+%2B+2x+%2B+1+=+1521+\"$
\n" ); document.write( " $\"+%28+x+%2B+1+%29%5E2+=+39%5E2+\"$
\n" ); document.write( " $\"+x+%2B+1++=+39+\"$
\n" ); document.write( " $\"+x+=+38+\"$
\n" ); document.write( "38 students were in the original group
\n" ); document.write( "--------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1900%2Fx+-+2.5+=+1900%2F%28+x+%2B+2+%29+\"$
\n" ); document.write( " $\"+1900%2F38+-+2.5+=+1900%2F%28+38+%2B+2+%29+\"$
\n" ); document.write( " $\"+50+-+2.5+=+1900%2F40+\"$
\n" ); document.write( " $\"+47.5+=+47.5+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );