document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155014>Question 155014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The tens digit of a number is 3 less than the units digit. If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3. 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 #114192 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=114192\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The tens digit of a number is 3 less than the units digit. If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3. What is the original number?<BR>\n" );
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document.write( "Let x = the 10's digit; Let y = units digit<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "10x+y = \"the number\"<BR>\n" );
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document.write( "\"The tens digit of a number is 3 less than the units digit.\",therefore<BR>\n" );
document.write( "x = (y-3)<BR>\n" );
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document.write( "\" If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3.<BR>\n" );
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document.write( "Subtract the remainder from the number and you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2810x%2By%29-3%29%2F%28%28x%2By%29%29 ALIGN=MIDDLE  ALT=\"%28%2810x%2By%29-3%29%2F%28%28x%2By%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4<BR>\n" );
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document.write( "multiply both sides by (x+y)<BR>\n" );
document.write( "10x + y - 3 = 4(x+y)<BR>\n" );
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document.write( "10x + y - 3 = 4x + 4y<BR>\n" );
document.write( "Arrange x on the left and y on the right with the remainder:<BR>\n" );
document.write( "10x - 4x = 4y - y + 3<BR>\n" );
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document.write( "6x = 3y + 3<BR>\n" );
document.write( "Substitute (y-3) for x:<BR>\n" );
document.write( "6(y-3) = 3y + 3<BR>\n" );
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document.write( "6y - 18 = 3y + 3<BR>\n" );
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document.write( "6y - 3y = 3 + 18<BR>\n" );
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document.write( "3y = 21<BR>\n" );
document.write( "y =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F3 ALIGN=MIDDLE  ALT=\"21%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 7<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x = 7 -3<BR>\n" );
document.write( "x = 4<BR>\n" );
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document.write( "47 = \"the number\"<BR>\n" );
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document.write( "Check solution in the statement:<BR>\n" );
document.write( "\"If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=47%2F%28%284%2B7%29%29 ALIGN=MIDDLE  ALT=\"47%2F%28%284%2B7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4, remainder of 3  </SPAN>\n" );
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