document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=48327>Question 48327</A>: <I><SPAN STYLE=\"word-break: break-all;\">   The sum of the digits of a two-digit no. is 11. If the digits are reversed the new no. is 7 more than twice the original no. Find the original no. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31958 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=31958\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, lets figure it out by \"looking\":\r<BR>\n" );
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document.write( "2 digits add to 11, so they must be one of the following 4 possibilities:<BR>\n" );
document.write( "29: 2+9 --> reversed is 92<BR>\n" );
document.write( "38: 3+8 --> reversed is 83<BR>\n" );
document.write( "47: 4+7 --> reversed is 74<BR>\n" );
document.write( "56: 5+6 --> reversed is 65\r<BR>\n" );
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document.write( "and twice 38 is 76. Then add 7 is 83. So the answer is 38.\r<BR>\n" );
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document.write( "Right then...mathematically:\r<BR>\n" );
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document.write( "Let the first number be xy and we are told that (x+y) = 11.\r<BR>\n" );
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document.write( "Also, x is the number of tens and y is the number of units. By this we mean that xy really means (10x+y).\r<BR>\n" );
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document.write( "If we reverse it, to yx, when then have the number (10y+x).\r<BR>\n" );
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document.write( "We are told that \"reversed number is twice original + 7\", so we need to convert this English to maths:\r<BR>\n" );
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document.write( "(reversed number) = twice(original number) + 7<BR>\n" );
document.write( "(10y+x) = 2(10x+y) + 7<BR>\n" );
document.write( "10y+x = 20x+2y + 7<BR>\n" );
document.write( "8y-19x = 7\r<BR>\n" );
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document.write( "So we have 2 equations now:<BR>\n" );
document.write( "x+y=11<BR>\n" );
document.write( "8y-19x = 7\r<BR>\n" );
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document.write( "scale up the first one by 8 --> 8x+8y = 88, giving us<BR>\n" );
document.write( "8x+8y = 88<BR>\n" );
document.write( "8y-19x = 7\r<BR>\n" );
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document.write( "Re-write the order:<BR>\n" );
document.write( "8y+8x = 88<BR>\n" );
document.write( "8y-19x = 7\r<BR>\n" );
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document.write( "Now lets subtract the equations, to get rid of the y terms.<BR>\n" );
document.write( "27x = 81<BR>\n" );
document.write( "x = 81/27<BR>\n" );
document.write( "x = 3\r<BR>\n" );
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document.write( "so from x+y=11 we have<BR>\n" );
document.write( "3+y=11<BR>\n" );
document.write( "--> y=8\r<BR>\n" );
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document.write( "So the original number, xy is 38.\r<BR>\n" );
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document.write( "jon. </SPAN>\n" );
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