document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=409090>Question 409090</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with a word problem. This is what I have so far:\r<BR>\n" );
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document.write( "Joe has a collection of nickels and dimes that is worth $3.95. If the number of dimes was doubled and the number of nickels was increased by 21, the value of the coins would be $8.40. How many nickels and dimes does he have?\r<BR>\n" );
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document.write( "first part:<BR>\n" );
document.write( "dimes value + nickles value = total amount<BR>\n" );
document.write( "(value of a dime)(# of dimes) + (value of a nickle)(# of nickles) = total amount<BR>\n" );
document.write( "(0.10)(# of dimes) + (0.05)(# of nickles) = 3.95<BR>\n" );
document.write( "(0.10)(d) + (0.05)(n) = 3.95<BR>\n" );
document.write( "so d = number of dimes we start with<BR>\n" );
document.write( "n = number of nickles we start with\r<BR>\n" );
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document.write( "second part:<BR>\n" );
document.write( "dimes value + nickles value = total amount<BR>\n" );
document.write( "(value of a dime)(# of dimes) + (value of a nickle)(# of nickles) = total amount<BR>\n" );
document.write( "(0.10)(2*d) + (0.05)(n + 21) = 8.40<BR>\n" );
document.write( "because we're supposed to have double (*2 the dimes) and 21 more nickles\r<BR>\n" );
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document.write( "The two equations are then:<BR>\n" );
document.write( "(0.10)(d) + (0.05)(n) = 3.95<BR>\n" );
document.write( "(0.10)(2d) + (0.05)(n + 21) = 8.40 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #288085 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=288085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "What you have done so far is absolutely spot on correct, but I'm going to show you a little trick that will get rid of all of the ugly decimal coefficients so that you are much less likely to make any arithmetic errors.\r<BR>\n" );
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document.write( "While it is true that a dime has a value of 0.10 dollars, it also can be said to have a value of 10 cents.  Likewise a nickel is worth 5 cents.  Furthermore, the total value of the coins in either situation can be said to be 395 cents or 840 cents.\r<BR>\n" );
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document.write( "Now we can write the equations as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10d\ +\ 5n\ =\ 395\">\r<BR>\n" );
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document.write( "And\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 20d\ +\ 5(n\ +\ 21)\ = 840\">\r<BR>\n" );
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document.write( "Much tidier, no?\r<BR>\n" );
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document.write( "A little manipulation gets us:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10d\ +\ 5n\ =\ 395\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 20d\ +\ 5n\ = 735\">\r<BR>\n" );
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document.write( "Multiply the first equation by -1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -10d\ -\ 5n\ =\ -395\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 20d\ +\ 5n\ = 735\">\r<BR>\n" );
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document.write( "Then add the two equations, term by term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10d\ +\ 0n\ =\ 340\">\r<BR>\n" );
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document.write( "And that leads us to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 34\">\r<BR>\n" );
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document.write( "Meaning we started with 34 dimes, and it should follow directly from that fact that we started with 11 nickels accounting for the 55 cents remaining in the $3.95.\r<BR>\n" );
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document.write( "Checking our work:  If we have twice the dimes, or 68 dimes, we have $6.80 in dimes and an additional 21 nickels would be 55 cents plus $1.05 or $1.60.  Finally, $6.80 plus $1.60 is indeed $8.40.  Ta Da!\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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