document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=619003>Question 619003</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number consist of three digits of whose sum is 17 the middle digit exceeds the sum of two digits by one if the digits of the number are reversed the number dimini shes by 396 find the number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389365 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=389365\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "A number consist of three digits of whose sum is 17 the middle digit exceeds the sum of two digits by one if the digits of the number are reversed the number dimini shes by 396 find the number?\r<BR>\n" );
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document.write( "Let the hundreds, tens, and units digits be H, T, & U, respectively<BR>\n" );
document.write( "Since the 3 digits sum to 17, then: H + T + U = 17 ------ eq (i)\r<BR>\n" );
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document.write( "Since the middle digit (T) exceeds the sum of the other 2 digits by 1, then: <BR>\n" );
document.write( "T = H + U + 1<BR>\n" );
document.write( "H – T + U = - 1 ---- eq (ii)\r<BR>\n" );
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document.write( "Since when number is reversed the number diminishes by 396, then: <BR>\n" );
document.write( "100U + 10T + H = 100H + 10T + U - 396<BR>\n" );
document.write( "H - 100H + 10T – 10T + 100U – U = - 396<BR>\n" );
document.write( "– 99H + 99U = - 396 <BR>\n" );
document.write( "99(- H + U) = 99(- 4) ----- Factoring out GCF, 99 <BR>\n" );
document.write( "- H + U = - 4 ----- eq (iii)\r<BR>\n" );
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document.write( "H + T + U = 17 ---- eq (i)<BR>\n" );
document.write( "H – T + U = - 1 ---- eq (ii)<BR>\n" );
document.write( "2H + 2U = 16 ----- Adding eqs (i) & (ii)<BR>\n" );
document.write( "2(H + U) = 2(8) ------ Factoring out GCF, 2<BR>\n" );
document.write( "H + U = 8 ------- eq (iv)<BR>\n" );
document.write( "- H + U = - 4 ----- eq (iii)<BR>\n" );
document.write( "2U = 4 ----- Adding eqs (iv) & (iii)<BR>\n" );
document.write( "U, or units digit = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F2 ALIGN=MIDDLE  ALT=\"4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%29 ALIGN=MIDDLE  ALT=\"highlight%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "H + 2 = 8 ----- Substituting 2 for U in eq (iv)<BR>\n" );
document.write( "H, or hundreds digit = 8 – 2, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%286%29 ALIGN=MIDDLE  ALT=\"highlight%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "6 + T + 2 = 17 ------ Substituting 2 for U, and 6 for H in eq (i)<BR>\n" );
document.write( "T = 17 – 8<BR>\n" );
document.write( "T, or tens digit = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289%29 ALIGN=MIDDLE  ALT=\"highlight%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The original number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28692%29 ALIGN=MIDDLE  ALT=\"highlight_green%28692%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at  MathMadEzy@aol.com </SPAN>\n" );
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