document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096585>Question 1096585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A two digit number is 3 more than 4 times the sum of its digits. if 18 is added tothis number, the sum is equal to the number obtained by interchanging the digits. 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 #711015 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=711015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>There are two distinct possible approaches to solving this problem:<br><BR>\n" );
document.write( "(1) Use algebra to find what 2-digit numbers have the property that the number is 3 more than 4 times the sum of its digits, and find which one of those numbers satisfies the property that adding 18 to the number produces a number which has the same digits in reverse order; or<br><BR>\n" );
document.write( "(2) Finding the 2-digit numbers which have the property  that adding 18 to the number produces a number which has the same digits in reverse order, and finding the one for which the number is 3 more than 4 times the sum of its digits.<br><BR>\n" );
document.write( "If you know the right number trick, the second option will get you to the answer much faster than the first.  But both methods are valid; and taking a look at both of them can be useful exercises.  So...<br><BR>\n" );
document.write( "(1) using algebra....<br><BR>\n" );
document.write( "If the 2-digit number has tens digit x and units digit y, then the value of the 2-digit number is 10x+y.  We want that to be equal to 3 more than 4 times the sum of x and y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2By+=+4%28x%2By%29%2B3 ALIGN=MIDDLE  ALT=\"10x%2By+=+4%28x%2By%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2By+=+4x%2B4y%2B3 ALIGN=MIDDLE  ALT=\"10x%2By+=+4x%2B4y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+=+3y%2B3 ALIGN=MIDDLE  ALT=\"6x+=+3y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+y%2B1 ALIGN=MIDDLE  ALT=\"2x+=+y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x-1 ALIGN=MIDDLE  ALT=\"y+=+2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We can easily list the combinations of x and y values that satisfy this equation and in which x and y are both single digits:<BR>\n" );
document.write( "x=1 --> y=1 --> the 2-digit number is 11<BR>\n" );
document.write( "x=2 --> y=3 --> the 2-digit number is 23<BR>\n" );
document.write( "x=3 --> y=5 --> the 2-digit number is 35<BR>\n" );
document.write( "x=4 --> y=7 --> the 2-digit number is 47<BR>\n" );
document.write( "x=5 --> y=9 --> the 2-digit number is 59<br><BR>\n" );
document.write( "Of those 2-digit numbers, there is only one which, when 18 is added to it, produces a 2-digit number with the two digits reversed: 35+18 = 53.<br><BR>\n" );
document.write( "So the 2-digit number we are looking for is 35.<br><BR>\n" );
document.write( "(2) the alternative method...<br><BR>\n" );
document.write( "If you have a 2-digit number, and adding 18 to the number produces a 2-digit number with the digits reversed, then the number has a tens digit which is 2 less than the units digit.  The 2-digit numbers with this property are<BR>\n" );
document.write( "13  24  35  46  57  68  79<br><BR>\n" );
document.write( "Checking these to find which of them has the property that the number is 3 more than 4 times the sum of its digits, we see that the only one satisfying that property is 35.<br><BR>\n" );
document.write( "So again by this method the number we are looking for is 35.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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