document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=436640>Question 436640</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a certain four-digit number is multiplied by 4 its digits appear in reverse order. It also has the following properties. Its first digit is a quarter of the last one. And its second digit is one less than the first. What number must it be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #302065 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=302065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When a certain four-digit number is multiplied by 4 its digits appear in reverse order.<BR>\n" );
document.write( " It also has the following properties. Its first digit is a quarter of the last one.<BR>\n" );
document.write( "And its second digit is one less than the first. What number must it be?<BR>\n" );
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document.write( "Let the four digit number = 1000a + 100b + 10c + d<BR>\n" );
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document.write( "\"When a four-digit number is multiplied by 4 its digits appear in reverse order.\"<BR>\n" );
document.write( "4(1000a+100b+10c+d) = 1000d + 100c + 10b + a<BR>\n" );
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document.write( "4000a + 400b + 40c + 4d = 1000d + 100c + 10b + a<BR>\n" );
document.write( "4000a - a + 400b - 10b = 100c - 40c + 1000d - 4d<BR>\n" );
document.write( "3999a + 390b = 60c + 996d<BR>\n" );
document.write( "Simplify, divide by 3<BR>\n" );
document.write( "1333a + 130b = 20c + 332d<BR>\n" );
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document.write( "\" Its first digit is a quarter of the last one.\"<BR>\n" );
document.write( "a = .25d<BR>\n" );
document.write( "or<BR>\n" );
document.write( "d = 4a<BR>\n" );
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document.write( "\"its second digit is one less than the first. <BR>\n" );
document.write( "b = (a-1)<BR>\n" );
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document.write( "1333a + 130b = 20c + 332d<BR>\n" );
document.write( "Replace b and d<BR>\n" );
document.write( "1333a + 130(a-1) = 20c + 332(4a)<BR>\n" );
document.write( "1333a + 130a - 130 = 20c + 1328a<BR>\n" );
document.write( "1333a + 130a - 1328a = 20c + 130<BR>\n" );
document.write( "135a = 20c + 130<BR>\n" );
document.write( "Simplify, divide by 5<BR>\n" );
document.write( "27a = 4c + 26<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F27 ALIGN=MIDDLE  ALT=\"4%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" >c + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%2F27 ALIGN=MIDDLE  ALT=\"26%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A close inspection of this equatiion reveals there is only one single digit integer solution<BR>\n" );
document.write( "c = 7; a = 2<BR>\n" );
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document.write( "find b and d<BR>\n" );
document.write( "b = 2 - 1<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "d = 4(2)<BR>\n" );
document.write( "d = 8<BR>\n" );
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document.write( "2178 is the number<BR>\n" );
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document.write( "Check this: 4 * 2178 = 8712 </SPAN>\n" );
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