document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142764>Question 142764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I know how to solve a linear equation with three variables by using two of the three equations to eliminate one variable and then use a different pair of equations to eliminate the same variable and then you can solve those equations. I am doing some word problems and writing the first two equations with three unknown variables is easy but I cannot seem to write the third.\r<BR>\n" );
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document.write( "Mike has 19 coins (nickels, dimes and quarters) in his piggy bank with a  total value of $2.35. There are 2 more dimes than nickels. How many of each type does Mike have?\r<BR>\n" );
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document.write( "N+D+Q=19<BR>\n" );
document.write( "5N+10D+25Q=235<BR>\n" );
document.write( "?\r<BR>\n" );
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document.write( "With the first two I can multiply the first by –5 to eliminate N. I need another equation. Help?\r<BR>\n" );
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document.write( "Fred, Tiger and Nancy play a round of golf together. Their combined score is 223. Fred’s score was 3 more than Nancy’s and Tiger’s score was 7 more than Fred’s. What was each person’s score. \r<BR>\n" );
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document.write( "You would think something simple like<BR>\n" );
document.write( "F=N+3<BR>\n" );
document.write( "T=F+7<BR>\n" );
document.write( "223=T+F+N\r<BR>\n" );
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document.write( "But I need three equations with three unknown variables. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103878 by </B><A HREF=/tutors/aboutme.mpl?userid=checkley77><B>checkley77(12844)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=checkley77><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=103878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> N+D+Q=19<BR>\n" );
document.write( "5N+10D+25Q=235<BR>\n" );
document.write( "D=N+2 IS THE THIRD EQUATION.<BR>\n" );
document.write( "N+(N+2)+Q=19<BR>\n" );
document.write( "2N+2+Q=19<BR>\n" );
document.write( "2N+Q=19-2<BR>\n" );
document.write( "2N+Q=17 MULTIPLY THIS EQUATION BY -25 & ADD IT TO THE [15N+25Q=215] EQUATION<BR>\n" );
document.write( "5N+10(N+2)+25Q=235<BR>\n" );
document.write( "5N+10N+20+25Q=235<BR>\n" );
document.write( "15N+25Q=235-20<BR>\n" );
document.write( "15N+25Q=215<BR>\n" );
document.write( "-50N-25Q=-425<BR>\n" );
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document.write( "-35N=-210<BR>\n" );
document.write( "N=-210/-35<BR>\n" );
document.write( "N=6 ANSWER FOR THE NUMBER OF NICKELS.<BR>\n" );
document.write( "D=6+2<BR>\n" );
document.write( "D=8 ANSWER FOR THE NUMBER OF DIMES.<BR>\n" );
document.write( "2*6+Q=17<BR>\n" );
document.write( "12+Q=17<BR>\n" );
document.write( "Q=17-12<BR>\n" );
document.write( "Q=5 NUMBER OF QUARTERS.<BR>\n" );
document.write( "PROOF:<BR>\n" );
document.write( "6+8+5=19<BR>\n" );
document.write( "19=19<BR>\n" );
document.write( "AND:<BR>\n" );
document.write( "5*6+10*8+25*5=235<BR>\n" );
document.write( "30+80+125=235<BR>\n" );
document.write( "235=235<BR>\n" );
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document.write( "YOU HAVE THE THREE REQUIRED EQUATION HOWEVER YOU DO NOT NEED ALL THREE VARIABLES IN EACH EQUATION. iN FACT IT IS EASIER TO SOLVE IF THERE ARE ONLY TWO VARIABLES.<BR>\n" );
document.write( "F=N+3<BR>\n" );
document.write( "T=F+7 OR T=(N+3)+7 OR T=N+10<BR>\n" );
document.write( "223=T+F+N OR 223=(N+10)+(N+3)+N<BR>\n" );
document.write( "223=N+10+N+3+N<BR>\n" );
document.write( "223=3N+13<BR>\n" );
document.write( "3N=223-13<BR>\n" );
document.write( "3N=210<BR>\n" );
document.write( "N=210/3<BR>\n" );
document.write( "N=70 FOR NANCY'S SCORE.<BR>\n" );
document.write( "F=70+3=73 FOR FRED'S SCORE.<BR>\n" );
document.write( "T=73+7=80 FOR TIGER'S SCORE.<BR>\n" );
document.write( "PROOF:<BR>\n" );
document.write( "223=70+73+80<BR>\n" );
document.write( "223=223<BR>\n" );
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