document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622057>Question 622057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the three-digit number which satisfies the following conditon? The  tens digit is greater than the ones digit, the sum of the digits is 9, and if the digits are reversed and the resulting three-digit number is subtracted fron the original number, the difference is 198. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391278 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=391278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what is the three-digit number which satisfies the following conditon? The  tens digit is greater than the ones digit, the sum of the digits is 9, and if the digits are reversed and the resulting three-digit number is subtracted fron the original number, the difference is 198.\r<BR>\n" );
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document.write( "Let hundreds, tens, and units digits be H, T, and U, respectively\r<BR>\n" );
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document.write( "H + T + U = 9 ------ eq (i)<BR>\n" );
document.write( "Original number: 100H + 10T + U<BR>\n" );
document.write( "Reversed number: 100U + 10T + H<BR>\n" );
document.write( "100H + 10T + U – (100U + 10T + H) = 198 ----- Subtracting reversed no. from original no.<BR>\n" );
document.write( "100H + 10T + U – 100U – 10T – H = 198<BR>\n" );
document.write( "99H – 99U = 198 ------ 99(H – U) = 99(2) ------ H – U = 2 eq (ii) \r<BR>\n" );
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document.write( "T > U<BR>\n" );
document.write( "H + T + U = 9 ----- eq (i)<BR>\n" );
document.write( "H – U = 2 ----- eq (ii)<BR>\n" );
document.write( "T + 2U = 7 ------ Subtracting eq (ii) from eq (i) ------ eq (iii)\r<BR>\n" );
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document.write( "From eq (iii), U CANNOT BE 9, 8, 7, 6, 5, or 0<BR>\n" );
document.write( "This means that U MUST either be 4, 3, 2, or 1\r<BR>\n" );
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document.write( "U = 4<BR>\n" );
document.write( "Based on the fact that T + 2U = 7, T = 7 – 8, or – 1 (NOT POSSIBLE)\r<BR>\n" );
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document.write( "U = 3<BR>\n" );
document.write( "Based on the fact that T + 2U = 7, T = 7 – 6, T = 1. But, T > U, so T CANNOT be 1 if U is 3\r<BR>\n" );
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document.write( "U = 2<BR>\n" );
document.write( "Based on the fact that T + 2U = 7, T = 7 – 4, T = 3. This is POSSIBLE, which means that H = 2 + 2, or 4, which means that original number’s 432. Reversed, it becomes 234. Difference = 198 (TRUE)\r<BR>\n" );
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document.write( "U = 1<BR>\n" );
document.write( "Based on the fact that T + 2U = 7, T = 7 – 2, or 5. This is POSSIBLE, which means that H = 2 + 1, or 3, which means that original number’s 351. Reversed, it becomes 153. Difference = 198 (TRUE).\r<BR>\n" );
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document.write( "This means that the original number can either be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28432%29 ALIGN=MIDDLE  ALT=\"highlight_green%28432%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28351%29 ALIGN=MIDDLE  ALT=\"highlight_green%28351%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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