document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203790>Question 1203790</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Bob has 3 more $10 notes than $2 notes. The total value of the $2 notes is $94 less than the total value of the $10 notes. How many $2 notes does he have.<BR>\n" );
document.write( "Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839624 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</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=839624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = number of $2 notes<BR>\n" );
document.write( "x+3 = number of $10 notes\r<BR>\n" );
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document.write( "2x = total value of the $2 notes<BR>\n" );
document.write( "Example: we have x = 7 of these notes, so 2x = 2*7 = 14 dollars is the subtotal for this category.\r<BR>\n" );
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document.write( "10(x+3) = value of the $10 notes only\r<BR>\n" );
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document.write( "The phrase \"<font color=blue>The total value of the $2 notes is $94 less than the total value of the $10 notes</font>\" translates to the equation<BR>\n" );
document.write( "2x = 10(x+3)-94\r<BR>\n" );
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document.write( "Let's isolate x.<BR>\n" );
document.write( "2x = 10(x+3)-94<BR>\n" );
document.write( "2x = 10x+30-94<BR>\n" );
document.write( "2x = 10x-64<BR>\n" );
document.write( "2x-10x = -64<BR>\n" );
document.write( "-8x = -64<BR>\n" );
document.write( "x = -64/(-8)<BR>\n" );
document.write( "x = 8<BR>\n" );
document.write( "Bob has eight $2 notes<BR>\n" );
document.write( "The value so far is 2x = 2*8 = 16 dollars.\r<BR>\n" );
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document.write( "Since he has 3 more $10 bills, he would have x+3 = 8+3 = 11 copies of $10 bills<BR>\n" );
document.write( "The value here is 10*11 = 110 dollars\r<BR>\n" );
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document.write( "Value of the $2 bills: $16<BR>\n" );
document.write( "Value of the $10 bills: $110<BR>\n" );
document.write( "The gap between these values is $94. This helps confirm we have the right answers.\r<BR>\n" );
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document.write( "Another way to verify would be to plug x = 8 into the original equation and simplify both sides.<BR>\n" );
document.write( "2x = 10(x+3)-94<BR>\n" );
document.write( "2*8 = 10(8+3)-94<BR>\n" );
document.write( "2*8 = 10(11)-94<BR>\n" );
document.write( "16 = 110-94<BR>\n" );
document.write( "16 = 16<BR>\n" );
document.write( "Everything works out.\r<BR>\n" );
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document.write( "Answer:  <font color=red size=4>8</font><BR>\n" );
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