document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203240>Question 1203240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are $925 in $5, $10, and $20 bills in a cash register. There is a total of 71 bills. The number of $20 bills is 7 less than the total number of $5 bills and $10 bills. How many bills of each denomination are in the cash register? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838655 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13334)</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=838655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The problem is more easily solved if you do a bit of logical reasoning and mental arithmetic before plunging into solving the problem with a system of 3 equations.<br><BR>\n" );
document.write( "The total number of bills is 71, and the number of $20 bills is 7 less than the total number of $5 and $10 bills.  A bit of mental arithmetic (or formal algebra, if you want) tells us that the number of $20 bills is 32 and the total number of $5 and $10 bills is 39.<br><BR>\n" );
document.write( "So now we have 32($20) = $640 in $20 bills and $925-$640 = $285 in $5 and $10 bills.<br><BR>\n" );
document.write( "For me, the easiest way to finish solving the problem is to first consider the case where there are 39 $5 bills, then see how many of those need to be replaced with $10 bills to make the required total of $285.<br><BR>\n" );
document.write( "39 $5 bills make a total of $195<BR>\n" );
document.write( "The actual total is $285, which is $90 more than $195<BR>\n" );
document.write( "Each time we replace a $5 bill with a $10 bill, the total increases by $5.  So the number of times we need to do that is $90/$5 = 18.  So the number of $10 bills is 18, leaving 39-18 = 21 $5 bills.<br><BR>\n" );
document.write( "ANSWER: 32 $20 bills, 18 $10 bills, and 21 $5 bills<br><BR>\n" );
document.write( "CHECK: 32($20)+18($10)+21($5)= $640+$180+$105 = $925<br><BR>\n" );
document.write( " </SPAN>\n" );
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