document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42827>Question 42827</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395771161/algebrahomeworkh>Algebra Structure and Method Book 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Jessica has 16 dimes and quarters. Whitney has twice as many dimes and 1/3 as many quarters as Jessica has. If they both have the same amount of money, what coins do each have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27890 by </B><A HREF=/tutors/aboutme.mpl?userid=aaaaaaaa><B>aaaaaaaa(138)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=aaaaaaaa><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=27890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's denote the number of dimes Jessica has by d and the number of quarters she has by q.\r<BR>\n" );
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document.write( "The first sentence tells us that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+%2B+q+=+16 ALIGN=MIDDLE  ALT=\"d+%2B+q+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Whitney has twice as many dimes (2d) and 1/3 as many quarters (1/3q) and they have the same amount of money. We could try to say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+%2B+q+=+2d+%2B+q%2F3 ALIGN=MIDDLE  ALT=\"d+%2B+q+=+2d+%2B+q%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but that's not true, as d and q have different value. Our equation, with the weight of the values in, is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d+%2B+25q+=+2%2A%2810d%29+%2B+25q%2F3 ALIGN=MIDDLE  ALT=\"10d+%2B+25q+=+2%2A%2810d%29+%2B+25q%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can simplify it by multiplying the 2, getting:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d+%2B+25q+=+20d+%2B+25q%2F3 ALIGN=MIDDLE  ALT=\"10d+%2B+25q+=+20d+%2B+25q%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then, we can  subtract 20d and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24q%2F3 ALIGN=MIDDLE  ALT=\"24q%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides of the equation and solve the system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10d+%2B+50q%2F3+=+0 ALIGN=MIDDLE  ALT=\"-10d+%2B+50q%2F3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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++++1%5Cd+%2B+1%5Cq+=+16%2C%0D%0A++++-10%5Cd+%2B+16.6666666666667%5Cq+=+0+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 1*q to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ad+=+16+-+1%2Aq ALIGN=MIDDLE  ALT=\"1%2Ad+=+16+-+1%2Aq\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+16%2F1+-+1%2Aq%2F1 ALIGN=MIDDLE  ALT=\"d+=+16%2F1+-+1%2Aq%2F1\"   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=-10%2A%2816%2F1+-+1%2Aq%2F1%29+%2B+16.6666666666667%5Cq+=+0 ALIGN=MIDDLE  ALT=\"-10%2A%2816%2F1+-+1%2Aq%2F1%29+%2B+16.6666666666667%5Cq+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that q=5.99999999999999. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+16%2F1+-+1%2Aq%2F1 ALIGN=MIDDLE  ALT=\"d+=+16%2F1+-+1%2Aq%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, d=10.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+d=10%2C+q=5.99999999999999+%29 ALIGN=MIDDLE  ALT=\"system%28+d=10%2C+q=5.99999999999999+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Therefore, Jessica has 10 dimes and 6 quarters, and Whitney has 2*10 = 20 dimes and 1/3 * 6 = 2 quarters.\r<BR>\n" );
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document.write( "We can check by seeing that 10*10 + 25*6 = 250, and 20*10 + 25*2 is also 250. </SPAN>\n" );
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