document.write( "Question 1159591: Please help me solve this word problem \r
\n" ); document.write( "\n" ); document.write( "Adams High prevailed in a track meet with the help of 20 individual-event placers earning a combined 68 points. A first-place finish earns 5 points, a second place finish earns 3 points, and a third-place finish earns 1 point. Adams had a strong second place showing, with as many second-place finishers as first-and third place finishers combined. Use a system of linear equations to model the data. Solve the system to find how many athletes finished in each place. \n" ); document.write( "
Algebra.Com's Answer #782899 by Boreal(15235)\"\" \"About 
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F+S+T=20
\n" ); document.write( "5F+3S+1T=68
\n" ); document.write( "but S=F+T
\n" ); document.write( "so the first may be written as
\n" ); document.write( "2F+2T=20
\n" ); document.write( "and the second as
\n" ); document.write( "8F+4T=68
\n" ); document.write( "-4F-4T=-40 multiplying the top by -2
\n" ); document.write( "4F=28
\n" ); document.write( "F=7 first places and 35 points
\n" ); document.write( "Now there is S+T=13
\n" ); document.write( "and 3S+1T=33 (points left)
\n" ); document.write( "and -S-T=-13
\n" ); document.write( "2S=20
\n" ); document.write( "S=10 second places
\n" ); document.write( "T=3 third places
\n" ); document.write( "!st place--7
\n" ); document.write( "2nd place-10
\n" ); document.write( "3rd place--3 \n" ); document.write( "
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