document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73620>Question 73620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following problem is not from a book.<BR>\n" );
document.write( "Jose has 6 more dimes than quaters. If his coins total $ 1.65. How many coins of each type does he have. My solution is 3 quaters and 9 dimes. However I can not put it into an equation.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52643 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let Q equal the unknown number of quarters he has and let D equal the unknown number of dimes.<BR>\n" );
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document.write( "Since he has 6 more dimes than quarters we can say that if we added 6 to the number of<BR>\n" );
document.write( "quarters that total would be the same as the number of dimes.  In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q+%2B+6+=+D ALIGN=MIDDLE  ALT=\"Q+%2B+6+=+D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We also know that he has 165 cents total. If we multiply the number of quarters that he has<BR>\n" );
document.write( "by 25 cents per quarter that will give us the total number of cents from quarters. In the<BR>\n" );
document.write( "same way, if we multiply the number of dimes times 10 cents per dime that will give us<BR>\n" );
document.write( "the number of cents from dimes.  Added together the number of cents from quarters and<BR>\n" );
document.write( "the number of cents from dimes must total 165.  In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825%2AQ%29%2B%2810%2AD%29+=+165 ALIGN=MIDDLE  ALT=\"%2825%2AQ%29%2B%2810%2AD%29+=+165\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "From our first equation we know that D = Q + 6.  Let's substitute Q + 6 for D in the second<BR>\n" );
document.write( "equation that talks about cents.  When we do that the second equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825%2AQ%29+%2B+10%2A%28Q+%2B+6%29+=+165 ALIGN=MIDDLE  ALT=\"%2825%2AQ%29+%2B+10%2A%28Q+%2B+6%29+=+165\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply on the left side to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2AQ+%2B+10%2AQ+%2B+60+=+165 ALIGN=MIDDLE  ALT=\"25%2AQ+%2B+10%2AQ+%2B+60+=+165\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add the two terms containing Q:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2AQ+%2B+60+=+165 ALIGN=MIDDLE  ALT=\"35%2AQ+%2B+60+=+165\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Eliminate the 60 on the left side by subtracting 60 from both sides of the equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2AQ+=+105 ALIGN=MIDDLE  ALT=\"35%2AQ+=+105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally divide both sides of this equation by 35 and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+105%2F35+=+3 ALIGN=MIDDLE  ALT=\"q+=+105%2F35+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So now we know that we have 3 quarters, just as you said. And since we know that we have<BR>\n" );
document.write( "6 more dimes than quarters we know the number of dimes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B3+=+9 ALIGN=MIDDLE  ALT=\"6%2B3+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "There's how you can get the answer of 3 quarters and 9 dimes.<BR>\n" );
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document.write( "Hope this helps you to understand how to get the answer by mathematics. </SPAN>\n" );
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