document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=340893>Question 340893</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of the three digits is 15.The sum of the first and third is twice the second.The sum of the second and third is one less than the first. Who Am I? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244179 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=244179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The product of the three digits is 15.The sum of the first and third is twice the second.The sum of the second and third is one less than the first. Who Am I?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3 digit number, product of the 3 digits is 15<BR>\n" );
document.write( "1st + 3rd = 2 * 2nd<BR>\n" );
document.write( "2nd + 3rd = 1st - 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let 3 digit numbers product = abc = 15<BR>\n" );
document.write( "a + c = 2b<BR>\n" );
document.write( "b + c = a - 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b + c = a - 1, solve for c<BR>\n" );
document.write( "c = a - b - 1, substitute this into a + c = 2b\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a + (a - b - 1) = 2b<BR>\n" );
document.write( "2a - b - 1 = 2b<BR>\n" );
document.write( "2a - 1 = 3b, solve for a<BR>\n" );
document.write( "2a = 3b + 1<BR>\n" );
document.write( "a = (3/2)b + 1/2, substitute into b + c = a - 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b + c = (3/2)b + 1/2 - 1<BR>\n" );
document.write( "b + c = (3/2)b - 1/2, solve for c<BR>\n" );
document.write( "c = (1/2)b - 1/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute a = (3/2)b + 1/2 & c = (1/2)b - 1/2 into abc = 15<BR>\n" );
document.write( "((3/2)b + 1/2) * b * ((1/2)b - 1/2) = 15<BR>\n" );
document.write( "((3/2)b + 1/2) * ((1/2)b^2 - (1/2)b) = 15<BR>\n" );
document.write( "use FOIL (First Outer Inner Last)<BR>\n" );
document.write( "3/2 * 1/2 * b^3 - 1/2 * 3/2 * b^2 + 1/2 * 1/2 * b^2 - 1/2 * 1/2 * b = 15<BR>\n" );
document.write( "1/2 * (3/2 * b^3 - 3/2 * b^2 + 1/2 * b^2 - 1/2 * b) = 15<BR>\n" );
document.write( "multiply both sides by 2<BR>\n" );
document.write( "3/2 * b^3 - 3/2 * b^2 + 1/2 * b^2 - 1/2 * b = 30<BR>\n" );
document.write( "3/2 * b^3 - 2/2 * b^2 - 1/2 * b = 30<BR>\n" );
document.write( "3/2 * b^3 - b^2 - 1/2 * b = 30<BR>\n" );
document.write( "multiply both sides by 2<BR>\n" );
document.write( "3b^3 - 2b^2 - b = 60<BR>\n" );
document.write( "b * (3b^2 - 2b - 1) = 60<BR>\n" );
document.write( "b * (3b + 1)(b - 1) = 60<BR>\n" );
document.write( "factor 60<BR>\n" );
document.write( "60 = 2 * 30 = 2 * 2 * 15 = 2 * 2 * 3 * 5 = 3 * 2 * 10 = 6 * 10<BR>\n" );
document.write( "b = 3, b - 1 = 2, 3b + 1 = 3 * 3 + 1 = 9 + 1 = 10, 3 * 10 * 2 = 30 * 2 = 60<BR>\n" );
document.write( "substitute b = 3 into a = (3/2)b + 1/2<BR>\n" );
document.write( "a = 3/2 * 3 + 1/2 = 9/2 + 1/2 = 10/2 = 5<BR>\n" );
document.write( "substitute a = 5 & b = 3 into abc = 15<BR>\n" );
document.write( "5 * 3 * c = 15<BR>\n" );
document.write( "15 * c = 15<BR>\n" );
document.write( "c = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the 3 digit number is 531\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "check:<BR>\n" );
document.write( "3 digit number, product of the 3 digits is 15 --> 5 * 3 * 1 = 15, yes<BR>\n" );
document.write( "1st + 3rd = 2 * 2nd --> 5 + 1 = 6 = 2 * 3 = 6, yes<BR>\n" );
document.write( "2nd + 3rd = 1st - 1 --> 3 + 1 = 4 = 5 - 1 = 4, yes\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );