document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122469>Question 1122469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> mathematical expression for a three-digit number whose hundred digits is half the tens digit and the tens digit is 2 more than the units digit </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #738597 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=738597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let x be the hundreds digit;<BR>\n" );
document.write( "then the tens digit is 2x (the tens digit is twice the hundreds digit);<BR>\n" );
document.write( "then the units digit is 2x-2 (it is 2 less than the tens digit)<br><BR>\n" );
document.write( "The value of the 3-digit number ABC is 100A+10B+C.  So an expression for the 3-digit number in this problem is<br><BR>\n" );
document.write( "100(x)+10(2x)+1(2x-2)<br><BR>\n" );
document.write( "Simplify if required....<br><BR>\n" );
document.write( "Note that x and 2x are both single-digit positive integers; that means x can have only the values 1, 2, 3, or 4.<br><BR>\n" );
document.write( "Those values of x in the expression shown will produce all of the 3-digit numbers that satisfy the conditions of the problem.<br><BR>\n" );
document.write( "120<BR>\n" );
document.write( "242<BR>\n" );
document.write( "364<BR>\n" );
document.write( "486<br><BR>\n" );
document.write( "Another completely different way to solve the problem is to make a list of the 3-digit numbers that satisfy the given conditions and find an algebraic expression that produces exactly that list.<br><BR>\n" );
document.write( "Making the list is relatively easy; choose a hundreds digit; then the tens digit is twice the hundreds digit; then the units digit is 2 less than the tens digit:<br><BR>\n" );
document.write( "1; 1*2 = 2; 2-2 - 0  -->  120<BR>\n" );
document.write( "2; 2*2 = 4; 4-2 = 2  -->  242<BR>\n" );
document.write( "3; 3*2 = 6; 6-2 = 4  -->  364<BR>\n" );
document.write( "4; 4*2 = 8; 8-2 = 6  -->  486<BR>\n" );
document.write( "5; 5*2 = 10 too big; the list is complete.<br><BR>\n" );
document.write( "The 3-digit numbers satisfying the given conditions are<br><BR>\n" );
document.write( "120, 242, 364, and 486.<br><BR>\n" );
document.write( "A bit of simple algebra, seeing the first number 120 and a common difference of 122 between successive numbers in the list, yields the linear expression<br><BR>\n" );
document.write( "122x-2<br><BR>\n" );
document.write( "which is the simplified form of the expression shown above.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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