document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=230228>Question 230228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The total value of the quarters and dimes in a coin bank is $8.00.  If the quarters were dimes and the dimes were quarters, the total value of the coins would be $6.35.  Find the number of quarters in the bank.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #170496 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=170496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The total value of the quarters and dimes in a coin bank is $8.00.  If the quarters were dimes and the dimes were quarters, the total value of the coins would be $6.35.  Find the number of quarters in the bank.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1.  Let x be the number of dimes\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2.  Let y be the number of quarters since there are 16 coins in all.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3.  Let 0.10x be the dollar value of dimes.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4.  Let 0.25y be the dollar value of quarters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  Then, 0.10x+0.25y=8.00  since the total value of the quarters and dimes in a coin bank is $8.00\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 6.  Then, 0.25x+0.10y=6.35 since if the quarters were dimes and the dimes were quarters, the total value of the coins would be $6.35\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 7.  From Steps 5 and 6, we have the following linear system of equations\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.10x+0.25y=8.00<BR>\n" );
document.write( "0.25x+0.10y=6.35\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solving yields the following steps:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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++++0.1%5Cx+%2B+0.25%5Cy+=+8%2C%0D%0A++++0.25%5Cx+%2B+0.1%5Cy+=+6.35+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 0.25*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1%2Ax+=+8+-+0.25%2Ay ALIGN=MIDDLE  ALT=\"0.1%2Ax+=+8+-+0.25%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F0.1+-+0.25%2Ay%2F0.1 ALIGN=MIDDLE  ALT=\"x+=+8%2F0.1+-+0.25%2Ay%2F0.1\"   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=0.25%2A%288%2F0.1+-+0.25%2Ay%2F0.1%29+%2B+0.1%5Cy+=+6.35 ALIGN=MIDDLE  ALT=\"0.25%2A%288%2F0.1+-+0.25%2Ay%2F0.1%29+%2B+0.1%5Cy+=+6.35\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=26. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F0.1+-+0.25%2Ay%2F0.1 ALIGN=MIDDLE  ALT=\"x+=+8%2F0.1+-+0.25%2Ay%2F0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=15.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=15%2C+y=26+%29 ALIGN=MIDDLE  ALT=\"system%28+x=15%2C+y=26+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 8.  ANSWER:  The number of dimes is 15 and the number of quarters is 26.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope the above steps and explanation were helpful.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And good luck in your studies!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
document.write( "\n" );
document.write( "http://www.FreedomUniversity.TV<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );