document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178821>Question 1178821</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Paul, a french cashier, needs change for his cash register at the Paris Cafe.<BR>\n" );
document.write( "He needs the following change for 50 Euros:<BR>\n" );
document.write( "2 Euro coins, <BR>\n" );
document.write( "1 Euro coins and <BR>\n" );
document.write( "50 cent coins. <BR>\n" );
document.write( "He receives a total of 44 coins. <BR>\n" );
document.write( "The amount of 2 Euro coins and the<BR>\n" );
document.write( "amount of 50 cent coins have the same amount of coins.<BR>\n" );
document.write( "Find out how many coins of each type he received.<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 #808256 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=808256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Using formal algebra and a single variable....<br><BR>\n" );
document.write( "Let x = number of 2-Euro coins<BR>\n" );
document.write( "Then x = number of 50-cent coins  (same as the number of 2-Euro coins)<BR>\n" );
document.write( "And 44-2x = number of 1-Euro coins  (44, minus the total number of 2-Euro and 50-cent coins)<br><BR>\n" );
document.write( "The total value is 50 Euros:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%29%2B.5%28x%29%2B1%2844-2x%29+=+50 ALIGN=MIDDLE  ALT=\"2%28x%29%2B.5%28x%29%2B1%2844-2x%29+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve using basic algebra; I leave that to you.<br><BR>\n" );
document.write( "Informally, using logical reasoning and a bit of mental arithmetic....<br><BR>\n" );
document.write( "Imagine 44 coins, all 1 Euro.  That makes a total of 44 Euros, which is 6 Euros short of the actual total.<BR>\n" );
document.write( "To increase the value of the total, replace two 1-Euro coins with one 2-Euro coin and one 50-cent coin.  That keeps the total number of coins at 44 but increases the total value by 50 cents.<BR>\n" );
document.write( "The number of times you need to do that to make the additional 6 Euros is 6/.5 = 12.<BR>\n" );
document.write( "So when the total is the correct 50 Euros, you have 12 2-Euro coins, 12 50-cent coins, and 44-24=20 1-Euro coins.<br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "2-Euro coins: 12<BR>\n" );
document.write( "1-Euro coins: 20<BR>\n" );
document.write( "50-cent coins: 12<br><BR>\n" );
document.write( "CHECK: 12(2)+20(1)+12(.5) = 24+20+6 = 50<br>\r<BR>\n" );
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