document.write( "Question 1040470: The organisers of an essay competition decide that a winner in the competition gets a prize of $100 and a participant who does not win gets a prize a $25. The total prize money distributed is $3000. Find the number of winners , if the total number of participants is 63. \n" ); document.write( "

Algebra.Com's Answer #655285 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+x+\"$ = the number of winners
\n" ); document.write( " $\"+63+-+x+\"$ = the number of non-winners
\n" ); document.write( "-----------------------------------
\n" ); document.write( "given:
\n" ); document.write( " $\"+100x+%2B+25%2A%28+63+-+x+%29+=+3000+\"$
\n" ); document.write( " $\"+100x+%2B+1575+-+25x+=+3000+\"$
\n" ); document.write( " $\"+75x+=+3000+-+1575+\"$
\n" ); document.write( " $\"+75x+=+1425+\"$
\n" ); document.write( " $\"+x+=+19+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+63+-+x+=+63+-+19+\"$
\n" ); document.write( " $\"+63+-+x+=+44+\"$
\n" ); document.write( "------------------
\n" ); document.write( "There are 19 winners
\n" ); document.write( "----------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+100x+%2B+25%2A%28+63+-+x+%29+=+3000+\"$
\n" ); document.write( " $\"+100%2A19+%2B+25%2A44+=+3000+\"$
\n" ); document.write( " $\"+1900+%2B+1100+=+3000+\"$
\n" ); document.write( " $\"+3000+=+3000+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );