document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141884>Question 1141884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $7.80. <BR>\n" );
document.write( "a) set up a system if equations to represent the situation. <BR>\n" );
document.write( "b) find the number of quarters in the bank. <BR>\n" );
document.write( "please give details, thankyou  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762529 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 6.90 = 690 cents.<BR>\n" );
document.write( "q is the number of quarters<BR>\n" );
document.write( "d is the number of dimes\r<BR>\n" );
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document.write( "you get two equations.\r<BR>\n" );
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document.write( "first equation is 25 * q + 10 * d = 690\r<BR>\n" );
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document.write( "this is because each quarter is worth 25 cents and each dime is worth 10 cents.\r<BR>\n" );
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document.write( "second equation is 10 * q + 25 * d = 780\r<BR>\n" );
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document.write( "this is because each quarter is worth 10 cents and each dime is worth 25 cents.\r<BR>\n" );
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document.write( "the number of quarters and dimes is the same.\r<BR>\n" );
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document.write( "what is changed is their value as stated in the problem statement.\r<BR>\n" );
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document.write( "your two equations that need to be solved simultaneously are:\r<BR>\n" );
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document.write( "25 * q + 10 * d = 690<BR>\n" );
document.write( "10 * q + 25 * d = 780\r<BR>\n" );
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document.write( "multiply both sides of the second equation by 2.5 and leave the first equation as is to get:\r<BR>\n" );
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document.write( "25 * q + 10 * d = 690<BR>\n" );
document.write( "25 * q + 62.5 * d = 1950\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( "52.5 * d = 1260\r<BR>\n" );
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document.write( "solve for d to get d = 24\r<BR>\n" );
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document.write( "the first equation of 25 * q + 10 * d = 690 becomes 25 * q + 10 * 24 = 690\r<BR>\n" );
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document.write( "simplify to get 25 * q + 240 = 690\r<BR>\n" );
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document.write( "subtract 240 from both sides to get 25 * q = 450\r<BR>\n" );
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document.write( "solve for q to get q = 18\r<BR>\n" );
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document.write( "you have 18 quarters and 24 dimes.\r<BR>\n" );
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document.write( "if the value of the quarters is 25 cents and the value of the dimes is 10 cents, the total value is 25 * 18 + 10 * 24 = 690.\r<BR>\n" );
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document.write( "if the value of the quarters is 10 cents and the value of the dimes is 25 cents, the total value is 10 * 18 + 25 * 24 = 780.\r<BR>\n" );
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document.write( "the solution is confirmed to be good.\r<BR>\n" );
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document.write( "the solution is that the number of quarters is 18.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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