document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263943>Question 263943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A collection of 65 coins consisting of dimes, quarters, and half-dollars has a value of $16.30. There are two times as many quarters as dimes. Find the number of each kind of coin. <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 #194439 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=194439\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A collection of 65 coins consisting of dimes, quarters, and half-dollars has a value of $16.30. There are two times as many quarters as dimes. Find the number of each kind of coin.\r<BR>\n" );
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document.write( "H half-dollar, Q quarter, D dime<BR>\n" );
document.write( "2 times as many quarters as dimes\r<BR>\n" );
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document.write( "H + Q + D = 65 (replace Q with 2*D)<BR>\n" );
document.write( "H + 2 * D + D = 65<BR>\n" );
document.write( "H + 3 * D = 65 (solve for H for later)<BR>\n" );
document.write( "H = 65 - 3 * D\r<BR>\n" );
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document.write( "0.50 * H + 0.25 * Q + 0.10 * D = 16.30 (multiply both sides by 100)<BR>\n" );
document.write( "50 * H + 25 * Q + 10 * D = 1630 (replace Q with 2*D)<BR>\n" );
document.write( "50 * H + 25 * (2 * D) + 10 * D = 1630<BR>\n" );
document.write( "50 * H + 50 * D + 10 * D = 1630<BR>\n" );
document.write( "50 * H + 60 * D = 1630 (divide both sides by 10)<BR>\n" );
document.write( "5 * H + 6 * D = 163 (plug in H = 65 - 3 * D)<BR>\n" );
document.write( "5 * (65 - 3 * D) + 6 * D = 163<BR>\n" );
document.write( "325 - 15 * D + 6 * D = 163<BR>\n" );
document.write( "325 - 9 * D = 163<BR>\n" );
document.write( "-9 * D = -162<BR>\n" );
document.write( " 9 * D =  162<BR>\n" );
document.write( "     D = 18<BR>\n" );
document.write( "plug in D = 18 into H = 65 - 3 * D<BR>\n" );
document.write( "H = 65 - 3 * 18<BR>\n" );
document.write( "H = 65 - 54<BR>\n" );
document.write( "H = 11\r<BR>\n" );
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document.write( "so we got 18 dimes<BR>\n" );
document.write( "and since we had twice as many quarters as dimes that would be 36 quarters\r<BR>\n" );
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document.write( "65 coins - 18 coins - 36 coins = 47 coins - 36 coins = 11 coins\r<BR>\n" );
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document.write( "check:<BR>\n" );
document.write( "0.50 * 11 + 0.25 * 36 + 0.10 * 18<BR>\n" );
document.write( "5.50 + 9.00 + 1.80<BR>\n" );
document.write( "14.50 + 1.80<BR>\n" );
document.write( "16.30 which is the amount we had and wanted\r<BR>\n" );
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