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 #838650 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3835)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=838650\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Hints:\r<BR>\n" );
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document.write( "a = number of 5's<BR>\n" );
document.write( "b = number of 10's<BR>\n" );
document.write( "c = number of 20's\r<BR>\n" );
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document.write( "a+b+c = 71 is one equation to form since there are 71 bills overall.\r<BR>\n" );
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document.write( "c = a+b-7 because of the sentence \"The number of $20 bills is 7 less than the total number of $5 bills and $10 bills\"\r<BR>\n" );
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document.write( "Another equation to form is 5a+10b+20c = 925 because there's $925 total in the cash register.<BR>\n" );
document.write( "5a = amount of money from the 5's only<BR>\n" );
document.write( "10b = amount of money from the 10's only<BR>\n" );
document.write( "20c = amount of money from the 20's only\r<BR>\n" );
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document.write( "So we have this system of equations<BR>\n" );
document.write( "a+b+c = 71<BR>\n" );
document.write( "c = a+b-7<BR>\n" );
document.write( "5a+10b+20c = 925\r<BR>\n" );
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document.write( "There are 3 equations and 3 unknowns.\r<BR>\n" );
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document.write( "Try to make an equivalent system such that there are 2 equations and 2 unknowns.<BR>\n" );
document.write( "Use the substitution property to replace every copy of 'c' in equation (1) with a+b-7. This gets rid of c and we're left with 'a's and 'b's only. Repeat the same idea for equation (3) as well.\r<BR>\n" );
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document.write( "I'll let the student take over from here.\r<BR>\n" );
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document.write( "Let me know if these hints help or not. <BR>\n" );
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