document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190271>Question 190271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.40. how many coins of each type did Sam find? : Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.40. how many coins of each type did Sam find? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142787 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=142787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #9  Q: <font color=red>Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.40. how many coins of each type did Sam find?</font>\r<BR>\n" );
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document.write( "A:\r<BR>\n" );
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document.write( "Let n=# of nickels, d=# of dimes, and q=# of quarters\r<BR>\n" );
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document.write( "Since \"He found six more dimes than nickels but three times as many quarters as dimes\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=n%2B6 ALIGN=MIDDLE  ALT=\"d=n%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=3d ALIGN=MIDDLE  ALT=\"q=3d\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We'll call these equations 1 and 2.\r<BR>\n" );
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document.write( "Furthermore, because \"The total value of the coins was $11.40\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05n%2B0.10d%2B0.25q=11.40 ALIGN=MIDDLE  ALT=\"0.05n%2B0.10d%2B0.25q=11.40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: the total value of the nickels alone is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05n ALIGN=MIDDLE  ALT=\"0.05n\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie the value of ONE nickel multiplied by the number of nickels). The same is applied to the dimes and quarters. These expressions are then added up to get the total value. This is probably where you're stuck.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05n%2B0.10d%2B0.25q=11.40 ALIGN=MIDDLE  ALT=\"0.05n%2B0.10d%2B0.25q=11.40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the last equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%280.05n%29%2B100%280.10d%29%2B100%280.25q%29=100%2811.40%29 ALIGN=MIDDLE  ALT=\"100%280.05n%29%2B100%280.10d%29%2B100%280.25q%29=100%2811.40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by 100 to make every number a whole number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d%2B25q=1140 ALIGN=MIDDLE  ALT=\"5n%2B10d%2B25q=1140\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply. Let's call this equation 3.\r<BR>\n" );
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document.write( "So we have the equations\r<BR>\n" );
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document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=n%2B6 ALIGN=MIDDLE  ALT=\"d=n%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=3d ALIGN=MIDDLE  ALT=\"q=3d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equation 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d%2B25q=1140 ALIGN=MIDDLE  ALT=\"5n%2B10d%2B25q=1140\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You may see this as a system of equations, which looks like\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28d=n%2B6%2Cq=3d%2C5n%2B10d%2B25q=1140%29 ALIGN=MIDDLE  ALT=\"system%28d=n%2B6%2Cq=3d%2C5n%2B10d%2B25q=1140%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d%2B25q=1140 ALIGN=MIDDLE  ALT=\"5n%2B10d%2B25q=1140\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the third equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d%2B25%2Ahighlight%28%283d%29%29=1140 ALIGN=MIDDLE  ALT=\"5n%2B10d%2B25%2Ahighlight%28%283d%29%29=1140\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=3d ALIGN=MIDDLE  ALT=\"q=3d\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice how the variable \"q\" is no longer in the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d%2B25%283d%29=1140 ALIGN=MIDDLE  ALT=\"5n%2B10d%2B25%283d%29=1140\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d%2B75d=1140 ALIGN=MIDDLE  ALT=\"5n%2B10d%2B75d=1140\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10%2Ahighlight%28%28n%2B6%29%29%2B75%2Ahighlight%28%28n%2B6%29%29=1140 ALIGN=MIDDLE  ALT=\"5n%2B10%2Ahighlight%28%28n%2B6%29%29%2B75%2Ahighlight%28%28n%2B6%29%29=1140\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=n%2B6 ALIGN=MIDDLE  ALT=\"d=n%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now the variable \"d\" is gone. \r<BR>\n" );
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document.write( "Now we're left with a simple equation with one unknown variable.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10%28n%2B6%29%2B75%28n%2B6%29=1140 ALIGN=MIDDLE  ALT=\"5n%2B10%28n%2B6%29%2B75%28n%2B6%29=1140\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10n%2B60%2B75n%2B450=1140 ALIGN=MIDDLE  ALT=\"5n%2B10n%2B60%2B75n%2B450=1140\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90n%2B510=1140 ALIGN=MIDDLE  ALT=\"90n%2B510=1140\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90n=1140-510 ALIGN=MIDDLE  ALT=\"90n=1140-510\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=510 ALIGN=MIDDLE  ALT=\"510\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90n=630 ALIGN=MIDDLE  ALT=\"90n=630\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%28630%29%2F%2890%29 ALIGN=MIDDLE  ALT=\"n=%28630%29%2F%2890%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=7 ALIGN=MIDDLE  ALT=\"n=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So this means that there are 7 nickels.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=n%2B6 ALIGN=MIDDLE  ALT=\"d=n%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=7%2B6 ALIGN=MIDDLE  ALT=\"d=7%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=7 ALIGN=MIDDLE  ALT=\"n=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=13 ALIGN=MIDDLE  ALT=\"d=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So there are 13 dimes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=3d ALIGN=MIDDLE  ALT=\"q=3d\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=3%2813%29 ALIGN=MIDDLE  ALT=\"q=3%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=13 ALIGN=MIDDLE  ALT=\"d=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=39 ALIGN=MIDDLE  ALT=\"q=39\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So there are 39 quarters.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So there are 7 nickels, 13 dimes and 39 quarters. </SPAN>\n" );
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