document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012061>Question 1012061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Harry has a collection of coins consisting of dimes and quarters whose value is $17.60. The number of quarters exceeds the number of dimes by 8. Find the number of coins of each kind in the collection. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627914 by </B><A HREF=/tutors/aboutme.mpl?userid=ValorousDawn><B>ValorousDawn(53)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ValorousDawn><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/cgi-bin/show-face.mpl?user=ValorousDawn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say our number of dimes is represented by the variable d, and quarters by the variable q. \r<BR>\n" );
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document.write( "If the number of quarters exceeds that of dimes by 8, we have the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=d%2B8 ALIGN=MIDDLE  ALT=\"q=d%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "We also have numeric values. Since a quarter is worth 25 cents, the total value is 0.25q. The same applies for dimes with 0.10d. We are told it adds to 17.60, so we have the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25q%2B0.10d=17.60 ALIGN=MIDDLE  ALT=\"0.25q%2B0.10d=17.60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We now have a system of linear equations. You can solve this with substitution.<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear.solver>Linear System solver (using determinant)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Cd+%2B+-1%5Cq+=+8%2C%0D%0A++++0.1%5Cd+%2B+0.25%5Cq+=+17.6+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Any system of equations:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++a%5B11%5D%2Ad+%2B+a%5B12%5D%2Aq+=+b%5B1%5D%2C%0D%0A++++a%5B21%5D%2Ad+%2B+a%5B22%5D%2Aq+=+b%5B2%5D%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  has solution<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++d+=+%28b%5B1%5D%2Aa%5B22%5D+-+b%5B2%5D%2Aa%5B12%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%2C%0D%0A++++q+=+%28a%5B11%5D%2Ab%5B2%5D+-+a%5B21%5D%2Ab%5B1%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  or<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++++d+=+%288%2A0.25+-+17.6%2A-1%29%2F%281%2A0.25-0.1%2A-1%29+=+56%2C%0D%0A++++++q+=+%281%2A17.6+-+0.1%2A8%29%2F%281%2A0.25-0.1%2A-1%29+=+48%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (d=56, q=48}<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Cd+%2B+-1%5Cq+=+8%2C%0D%0A++++0.1%5Cd+%2B+0.25%5Cq+=+17.6+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving -1*q to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ad+=+8+-+-1%2Aq ALIGN=MIDDLE  ALT=\"1%2Ad+=+8+-+-1%2Aq\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+8%2F1+-+-1%2Aq%2F1 ALIGN=MIDDLE  ALT=\"d+=+8%2F1+-+-1%2Aq%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1%2A%288%2F1+-+-1%2Aq%2F1%29+%2B+0.25%5Cq+=+17.6 ALIGN=MIDDLE  ALT=\"0.1%2A%288%2F1+-+-1%2Aq%2F1%29+%2B+0.25%5Cq+=+17.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that q=48. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+8%2F1+-+-1%2Aq%2F1 ALIGN=MIDDLE  ALT=\"d+=+8%2F1+-+-1%2Aq%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, d=56.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+d=56%2C+q=48+%29 ALIGN=MIDDLE  ALT=\"system%28+d=56%2C+q=48+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( " </SPAN>\n" );
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