document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=808961>Question 808961</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the tens digit of a three-digit number is 3 less than 5 times the unit digit. three times the sum of the digits is 2 more than 4 times the hundreds digit. if the digits are reversed, the new number is 549 less than than the original number. what is the original number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #487648 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=487648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a = the 100's digit<BR>\n" );
document.write( "b = the 10's<BR>\n" );
document.write( "c = the units<BR>\n" );
document.write( "then<BR>\n" );
document.write( "100a+10b+c = the number<BR>\n" );
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document.write( "Write an equation for each statement:<BR>\n" );
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document.write( "\" the tens digit of a three-digit number is 3 less than 5 times the unit digit.\"<BR>\n" );
document.write( "b = (5c-3)\r<BR>\n" );
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document.write( "\" three times the sum of the digits is 2 more than 4 times the hundreds digit.\"<BR>\n" );
document.write( "3(a+b+c) = 4a + 2<BR>\n" );
document.write( "3a + 3b + 3c = 4a + 2<BR>\n" );
document.write( "3a - 4a + 3b + 3c = 2<BR>\n" );
document.write( "-a + 3b + 3c = 2<BR>\n" );
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document.write( "\"if the digits are reversed, the new number is 594 less than than the original number.\"<BR>\n" );
document.write( "100c + 10b + a = 100a + 10b + c - 594<BR>\n" );
document.write( "100c - c + 10c - 10c + a - 100a = -594<BR>\n" );
document.write( "99c - 99a = -594<BR>\n" );
document.write( "simplify, divide by 99<BR>\n" );
document.write( "c - a = -6<BR>\n" );
document.write( "mult by -1<BR>\n" );
document.write( "a - c = 6<BR>\n" );
document.write( "a = (c+6)<BR>\n" );
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document.write( "Now we have three equations<BR>\n" );
document.write( "b = (5c-3); -a + 3b + 3c = 2; a = (c+6)<BR>\n" );
document.write( "In the middle equation, replace a and b<BR>\n" );
document.write( "-(c+6) + 3(5c-3) + 3c = 2<BR>\n" );
document.write( "-c - 6 + 15c - 9 + 3c = 2<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "17c - 15 = 2<BR>\n" );
document.write( "17c = 2 + 15<BR>\n" );
document.write( "17c = 17<BR>\n" );
document.write( "c = 1<BR>\n" );
document.write( "then<BR>\n" );
document.write( "b = 5(1) - 3<BR>\n" );
document.write( "b = 2<BR>\n" );
document.write( "and<BR>\n" );
document.write( "a = 1 + 6<BR>\n" );
document.write( "a = 7<BR>\n" );
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document.write( "Our number then is 721<BR>\n" );
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document.write( "Check this in the 3rd statement: <BR>\n" );
document.write( "127 = 721 - 594<BR>\n" );
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document.write( "  </SPAN>\n" );
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