document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=223797>Question 223797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A mixture of dimes and quarters has a total value of $10.20. There are 57 coins in all. How many of each type are present? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167281 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A mixture of dimes and quarters has a total value of $10.20. There are 57 coins in all. How many of each type are present?\r<BR>\n" );
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document.write( "Step 1.  Let x be the number of quarters.\r<BR>\n" );
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document.write( "Step 2.  Let 0.25x be the dollar value of quarters.\r<BR>\n" );
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document.write( "Step 3.  Let y be the number of dimes.\r<BR>\n" );
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document.write( "Step 4.  Let 0.10y be the dollar value of dimes.\r<BR>\n" );
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document.write( "Step 5.  Then 0.25x+0.10y=10.20 be the total dollar value.\r<BR>\n" );
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document.write( "Step 6.  Also, x+y=57  since there are 57 coins\r<BR>\n" );
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document.write( "Step 7.  Our linear system of equation is given in Steps 4 and 5 is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25x%2B0.10y=10.20 ALIGN=MIDDLE  ALT=\"0.25x%2B0.10y=10.20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=57 ALIGN=MIDDLE  ALT=\"x%2By=57\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<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++++0.25%5Cx+%2B+0.1%5Cy+=+10.2%2C%0D%0A++++1%5Cx+%2B+1%5Cy+=+57+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 0.1*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25%2Ax+=+10.2+-+0.1%2Ay ALIGN=MIDDLE  ALT=\"0.25%2Ax+=+10.2+-+0.1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10.2%2F0.25+-+0.1%2Ay%2F0.25 ALIGN=MIDDLE  ALT=\"x+=+10.2%2F0.25+-+0.1%2Ay%2F0.25\"   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=1%2A%2810.2%2F0.25+-+0.1%2Ay%2F0.25%29+%2B+1%5Cy+=+57 ALIGN=MIDDLE  ALT=\"1%2A%2810.2%2F0.25+-+0.1%2Ay%2F0.25%29+%2B+1%5Cy+=+57\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=27. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10.2%2F0.25+-+0.1%2Ay%2F0.25 ALIGN=MIDDLE  ALT=\"x+=+10.2%2F0.25+-+0.1%2Ay%2F0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=30.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=30%2C+y=27+%29 ALIGN=MIDDLE  ALT=\"system%28+x=30%2C+y=27+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "So x=30 and y=27.  The difference is 3 and the total dollar value is 0.25*30+0.10*27=7.50+2.70=10.20 which is a true statement.  And the total number of coins is 57.\r<BR>\n" );
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document.write( "Step 8.  ANSWER:  The number of quarters is 30 and the number of dimes is 27.\r<BR>\n" );
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document.write( "I hope the above steps were helpful.\r<BR>\n" );
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document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit \r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit \r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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document.write( " </SPAN>\n" );
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