document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177887>Question 177887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A coin bank contains only qurarters and dimes. The total value of the coins is $10.40. If the dimes were quarters and the quarters were dimes the total value  of the coins would be $9.20. Find the total number of dimes in the bank. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132870 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=132870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let d = dimes<BR>\n" );
document.write( "and q = quarters<BR>\n" );
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document.write( "Since we have two unknowns we'll need two equations.<BR>\n" );
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document.write( "From: \"The total value of the coins is $10.40.\"<BR>\n" );
document.write( ".10d + .25q = 10.40 (equation 1)<BR>\n" );
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document.write( "From: \"If the dimes were quarters and the quarters were dimes the total value of the coins would be $9.20\"<BR>\n" );
document.write( ".25d + .10q = 9.20 (equation 2)<BR>\n" );
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document.write( "Using Cramer's rule:<BR>\n" );
document.write( "Determinant of coefficients:<BR>\n" );
document.write( "(.10)(.10)-(.25)(.25)<BR>\n" );
document.write( "=(0.01)-(0.0625)<BR>\n" );
document.write( "=-0.0525<BR>\n" );
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document.write( "Determinant of d:<BR>\n" );
document.write( "(10.40)(.10)-(9.20)(.25)<BR>\n" );
document.write( "=(1.04)-(2.3)<BR>\n" );
document.write( "=-1.26<BR>\n" );
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document.write( "Determinant of q:<BR>\n" );
document.write( "(.10)(9.20)-(.25)(10.40)<BR>\n" );
document.write( "=(.10)(9.20)-(.25)(10.40)<BR>\n" );
document.write( "=(.92)-(2.6)<BR>\n" );
document.write( "= -1.68<BR>\n" );
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document.write( "d = Detd/DetCoeff<BR>\n" );
document.write( "d = -1.26/-0.0525<BR>\n" );
document.write( "d = 24 (number of dimes)<BR>\n" );
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document.write( "q = Detq/DetCoeff<BR>\n" );
document.write( "q = -1.68/-0.0525<BR>\n" );
document.write( "q = 32 (number of quarters) </SPAN>\n" );
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