document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135924>Question 135924</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ten's digit of a certain two digit number is twice the units digit.If the number is multiplied by the sum of its digits the result is 63.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 #99585 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let x=the tens digit<BR>\n" );
document.write( "Ane let y=the units digit\r<BR>\n" );
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document.write( "Now we are told that:\r<BR>\n" );
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document.write( "x=2y---------------------------eq1\r<BR>\n" );
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document.write( "The sum of its digits is x+y and the number is 10x+y, ok?<BR>\n" );
document.write( "And we are being told that:\r<BR>\n" );
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document.write( "(x+y)(10x+y)=63  using the FOIL (First, Outer, Inner, Last) crutch we get:\r<BR>\n" );
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document.write( "10x^2+xy+10xy+y^2=63 and this equals<BR>\n" );
document.write( "10x^2+11xy+y^2=63--------------------------eq2\r<BR>\n" );
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document.write( "substitute x=2y from eq1 into eq2<BR>\n" );
document.write( "10(2y)^2+11(2y)(y)+y^2=63 simplify\r<BR>\n" );
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document.write( "40y^2+22y^2+y^2=63  collect like terms\r<BR>\n" );
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document.write( "63y^2=63  divide each side by 63\r<BR>\n" );
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document.write( "y^2=1  take square root of each side<BR>\n" );
document.write( "y=+ or - 1 so<BR>\n" );
document.write( "y=+1<BR>\n" );
document.write( "and y=-1<BR>\n" );
document.write( "And substituting these into eq1, we get:<BR>\n" );
document.write( "x=+2, when y=+1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=-2, when y=-1\r<BR>\n" );
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document.write( "So our answer is +21\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "Lets look at +21  <BR>\n" );
document.write( "2 is twice 1 so first condition is met; if the number is multiplied by the sum of its digits, the result is 63---3*21 is 63 so the second condition is met \r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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