document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113520>Question 113520</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0071435336/algebrahomeworkh>Arithmetic and algebra again</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the digits of a two-digit number is 7. If the digits are reversed, the new number increased by 3 equals 4 times the original number. Find the original number.\r<BR>\n" );
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document.write( "here is what I have done:\r<BR>\n" );
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document.write( "original number       10x + y     <BR>\n" );
document.write( "     new number       10y + x\r<BR>\n" );
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document.write( "x + y = 7\r<BR>\n" );
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document.write( "      <BR>\n" );
document.write( "      10x + y = 10y + x + 3<BR>\n" );
document.write( "10x -x + y -y = 10y -y + x -x + 3<BR>\n" );
document.write( "           9x =  9y + 3<BR>\n" );
document.write( "            x =   y + 3\r<BR>\n" );
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document.write( "            x + y = 7<BR>\n" );
document.write( "        (y+3) + y = 7<BR>\n" );
document.write( "           2y + 3 = 7<BR>\n" );
document.write( "         2y +3 -3 = 7 -3<BR>\n" );
document.write( "               2y = 4<BR>\n" );
document.write( "             2y/2 = 4/2<BR>\n" );
document.write( "                y = 2\r<BR>\n" );
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document.write( "            x + y = 7<BR>\n" );
document.write( "            2 + y = 7<BR>\n" );
document.write( "         2 -2 + y = 7 -2\r<BR>\n" );
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document.write( "                y = 5<BR>\n" );
document.write( "                x = 2\r<BR>\n" );
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document.write( "I get an answer, but it don't check.<BR>\n" );
document.write( "Every time I do this problem this my answer or fractional. please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82620 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82620\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here is one more solution to this problem...\r<BR>\n" );
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document.write( "Let ten's digit be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and unit's digit be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sum ALIGN=MIDDLE  ALT=\"Sum\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the digits = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y ALIGN=MIDDLE  ALT=\"x+%2B+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The number is = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x+%2B+y ALIGN=MIDDLE  ALT=\"10x+%2B+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sum ALIGN=MIDDLE  ALT=\"Sum\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the digits is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+7 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >…………………………………..…(1)\r<BR>\n" );
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document.write( "When the digits are reversed, the new number becomes\r<BR>\n" );
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document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10y+%2B+x ALIGN=MIDDLE  ALT=\"10y+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "New number increased by 3 = 4 times the original number\r<BR>\n" );
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document.write( " (10y + x) + 3 = 4 (10x + y)\r<BR>\n" );
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document.write( "or 10y + x + 3 = 40x + 4y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10y+%2B+x+-+40x+-+4y+=+-3 ALIGN=MIDDLE  ALT=\"10y+%2B+x+-+40x+-+4y+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-39x+%2B+6y+=+-3 ALIGN=MIDDLE  ALT=\"-39x+%2B+6y+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-13x+%2B+2y+=+-1 ALIGN=MIDDLE  ALT=\"-13x+%2B+2y+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >…… (Dividing by 3) …(2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Multiplying ALIGN=MIDDLE  ALT=\"Multiplying\"   DISABLED_style= \"max-width:90%; height:auto;\" > (1) by 2, we get,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+2y+=+14 ALIGN=MIDDLE  ALT=\"2x+%2B+2y+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >………………………………..…(3)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Subtracting ALIGN=MIDDLE  ALT=\"Subtracting\"   DISABLED_style= \"max-width:90%; height:auto;\" > (3) from (2),\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-13x+%2B+2y+=+-1 ALIGN=MIDDLE  ALT=\"-13x+%2B+2y+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >………………..……………..(2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+2y+=+14 ALIGN=MIDDLE  ALT=\"2x+%2B+2y+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >………………………………..…(3)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15x+=+-+15 ALIGN=MIDDLE  ALT=\"-15x+=+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > …….=>……<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in (1) we will have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+y+=+7 ALIGN=MIDDLE  ALT=\"1+%2B+y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ……=>…<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6 ALIGN=MIDDLE  ALT=\"y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, the number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x+%2B+y+=+10+x+1+%2B+6+=+16 ALIGN=MIDDLE  ALT=\"10x+%2B+y+=+10+x+1+%2B+6+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "	<BR>\n" );
document.write( "When the digits are reversed, the new number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810y+%2B+x%29+=+61 ALIGN=MIDDLE  ALT=\"%2810y+%2B+x%29+=+61\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810y+%2B+x%29+%2B+3+=+4+%2810x+%2B+y%29 ALIGN=MIDDLE  ALT=\"%2810y+%2B+x%29+%2B+3+=+4+%2810x+%2B+y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61+%2B+3+=+4+%2A16 ALIGN=MIDDLE  ALT=\"61+%2B+3+=+4+%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+=+64 ALIGN=MIDDLE  ALT=\"64+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
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