document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224659>Question 224659</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jake has 205 coins consisting of nickels, dimes, and quarters. If the total value of the coins is $22 and there are three times as many dimes as nickels, how many of each coin did he have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167850 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=167850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Jake has 205 coins consisting of nickels, dimes, and quarters. If the total value of the coins is $22 and there are three times as many dimes as nickels, how many of each coin did he have?\r<BR>\n" );
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document.write( "Step 1.  Let x be the number of nickels.\r<BR>\n" );
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document.write( "Step 2.  Let 0.05x be the dollar value of nickels.\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.  Let z be the number of quarters.\r<BR>\n" );
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document.write( "Step 6.  Let 0.25z be the dollar value of quarters.\r<BR>\n" );
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document.write( "Step 7.  Then x+y+z=205 since the total number of coins is 205.\r<BR>\n" );
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document.write( "Step 8.  Then  0.05x+0.10y+0.25z=22 since the dollar value of nickels, dimes, and quarters is 22.\r<BR>\n" );
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document.write( "Step 9.  We are also given y=3x since there are three times as many dimes as nickels.\r<BR>\n" );
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document.write( "Step 10.  Here's our system of linear equations given in Steps 7, 8, and 9.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=205 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=205\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation A<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05x%2B0.10y%2B0.25z=22 ALIGN=MIDDLE  ALT=\"0.05x%2B0.10y%2B0.25z=22\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation B<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x ALIGN=MIDDLE  ALT=\"y=3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation C\r<BR>\n" );
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document.write( "Substitute Equation C into Equations A and B\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3x%2Bz=205 ALIGN=MIDDLE  ALT=\"x%2B3x%2Bz=205\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2Bz=205 ALIGN=MIDDLE  ALT=\"4x%2Bz=205\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation A1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05x%2B0.10%283x%29%2B0.25z=22 ALIGN=MIDDLE  ALT=\"0.05x%2B0.10%283x%29%2B0.25z=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.35x%2B.25z=22 ALIGN=MIDDLE  ALT=\"0.35x%2B.25z=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > Equation B1\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++++4%5Cx+%2B+1%5Cz+=+205%2C%0D%0A++++0.35%5Cx+%2B+0.25%5Cz+=+22+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 1*z to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax+=+205+-+1%2Az ALIGN=MIDDLE  ALT=\"4%2Ax+=+205+-+1%2Az\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+205%2F4+-+1%2Az%2F4 ALIGN=MIDDLE  ALT=\"x+=+205%2F4+-+1%2Az%2F4\"   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=0.35%2A%28205%2F4+-+1%2Az%2F4%29+%2B+0.25%5Cz+=+22 ALIGN=MIDDLE  ALT=\"0.35%2A%28205%2F4+-+1%2Az%2F4%29+%2B+0.25%5Cz+=+22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that z=25. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+205%2F4+-+1%2Az%2F4 ALIGN=MIDDLE  ALT=\"x+=+205%2F4+-+1%2Az%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=45.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=45%2C+z=25+%29 ALIGN=MIDDLE  ALT=\"system%28+x=45%2C+z=25+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=45 ALIGN=MIDDLE  ALT=\"x=45\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=25 ALIGN=MIDDLE  ALT=\"z=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >  then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=205-45-25=135 ALIGN=MIDDLE  ALT=\"y=205-45-25=135\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check dollar value...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2A0.05%2B135%2A0.10%2B25%2A0.25=+2.25%2B13.50%2B6.25=22 ALIGN=MIDDLE  ALT=\"45%2A0.05%2B135%2A0.10%2B25%2A0.25=+2.25%2B13.50%2B6.25=22\"   DISABLED_style= \"max-width:90%; height:auto;\" >...which is a true statement.\r<BR>\n" );
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document.write( "Step 11.  ANSWER:  The number of nickels is 45, the number of dimes is 135, and the number of quarters is 25.\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 http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit 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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