document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270802>Question 270802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag of coins contains nickels, dimes, and quarters. There are a total of 17 coins in the bag, and the total amount of money in the bag is $2.00. There is one more dime than there are nickels. How many dimes, nickels, and quarters are in the bag? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198320 by </B><A HREF=/tutors/aboutme.mpl?userid=craigt><B>craigt(10)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=craigt><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=198320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Define the variables:<BR>\n" );
document.write( "x = The number of Nickels<BR>\n" );
document.write( "y = The number of Dimes<BR>\n" );
document.write( "z = The number of Quarters<BR>\n" );
document.write( "Define what you know based on the information given as a formula:<BR>\n" );
document.write( "1. The total number of coins is 17:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=17 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There is one more dime than nickels:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B1 ALIGN=MIDDLE  ALT=\"y=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2By%2B0z=1 ALIGN=MIDDLE  ALT=\"-x%2By%2B0z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The total of all coins is $2. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05x%2B.10y%2B.25z=2.00 ALIGN=MIDDLE  ALT=\".05x%2B.10y%2B.25z=2.00\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To make this last formula easier to work with, multiply both sides by 100 to<BR>\n" );
document.write( "eliminate the decimal places.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B10y%2B25y=200 ALIGN=MIDDLE  ALT=\"5x%2B10y%2B25y=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "So here is our system of equations:<BR>\n" );
document.write( "1.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=17 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2By%2B0z=1 ALIGN=MIDDLE  ALT=\"-x%2By%2B0z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B10y%2B25z=200 ALIGN=MIDDLE  ALT=\"5x%2B10y%2B25z=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "We were given information to express y in terms of x, so if we can solve for z in terms of x, then we can simply substitute and solve for x.<BR>\n" );
document.write( "There are a couple ways to do this. Equations 1 & 2 make it easy to eliminate one of the variables. By adding the two, you can eliminate x and by subtracting 2. from 1. you can eliminate y. By eliminating the x, we would be adding an extra step, so we would like to subtract eq.2 from eq.1 so we can define z in terms of x:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=17 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=17\"   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%2B0z=1 ALIGN=MIDDLE  ALT=\"-x%2By%2B0z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B0y%2Bz=16 ALIGN=MIDDLE  ALT=\"2x%2B0y%2Bz=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for z:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=16-2x ALIGN=MIDDLE  ALT=\"z=16-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We already solved for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B1 ALIGN=MIDDLE  ALT=\"y=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute into equation 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B10%28x%2B1%29%2B25%2816-2x%29=200 ALIGN=MIDDLE  ALT=\"5x%2B10%28x%2B1%29%2B25%2816-2x%29=200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B10x%2B10%2B400-50x=200 ALIGN=MIDDLE  ALT=\"5x%2B10x%2B10%2B400-50x=200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-35x%2B410=200 ALIGN=MIDDLE  ALT=\"-35x%2B410=200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-35x=-210 ALIGN=MIDDLE  ALT=\"-35x=-210\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then substitute 6 for x: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6%2B1 ALIGN=MIDDLE  ALT=\"y=6%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7 ALIGN=MIDDLE  ALT=\"y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Again, substitue 6 for x, now to solve for z: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=16-%282%2A6%29 ALIGN=MIDDLE  ALT=\"z=16-%282%2A6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=4 ALIGN=MIDDLE  ALT=\"z=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "To check your answers, substitute x, y, and z back into our known formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=17 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B7%2B4=17 ALIGN=MIDDLE  ALT=\"6%2B7%2B4=17\"   DISABLED_style= \"max-width:90%; height:auto;\" > True<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05x%2B.10y%2B.25z=2 ALIGN=MIDDLE  ALT=\".05x%2B.10y%2B.25z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05%286%29%2B.1%287%29%2B.25%284%29=2.00 ALIGN=MIDDLE  ALT=\".05%286%29%2B.1%287%29%2B.25%284%29=2.00\"   DISABLED_style= \"max-width:90%; height:auto;\" > True<BR>\n" );
document.write( "Answer: 6 Nickels, 7 Dimes, & 4 Quarters\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );