document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=507472>Question 507472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> it is a 4 digit number. the 2 digit is two times greater than the 3. the sum of all digits is three times than the last digit of the number. the product of the 3 and 4 digit is 12 times bigger than the ratio of the 2 to 3.? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #340573 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=340573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation for each statement, simplify and substitute if possible:<BR>\n" );
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document.write( "It is a 4 digit number.<BR>\n" );
document.write( "a, b, c, d; are the digits<BR>\n" );
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document.write( "The 2nd digit is two times greater than the 3rd.<BR>\n" );
document.write( "b = 2c<BR>\n" );
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document.write( "the sum of all digits is three times than the last digit of the number.<BR>\n" );
document.write( "a + b + c + d = 3d<BR>\n" );
document.write( "a + b + c = 3d - d<BR>\n" );
document.write( "a + b + c = 2d<BR>\n" );
document.write( "substitute 2c for b<BR>\n" );
document.write( "a + 2c + c = 2d<BR>\n" );
document.write( "a + 3c = 2d<BR>\n" );
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document.write( "the product of the 3 and 4 digit is 12 times bigger than the ratio of the 2nd to 3rd.?<BR>\n" );
document.write( "c*d = 12(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fc ALIGN=MIDDLE  ALT=\"b%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Replace b with 2c<BR>\n" );
document.write( "c*d = 12(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282c%29%2Fc ALIGN=MIDDLE  ALT=\"%282c%29%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Cancel c and we have<BR>\n" );
document.write( "c*d = 24<BR>\n" );
document.write( "We have 4 unknowns and 3 equations, so we will have to make an logical guess<BR>\n" );
document.write( "c=3, d=8; seems logical (d has to be the larger factor)<BR>\n" );
document.write( "Go with that and using the 2nd equation we have:<BR>\n" );
document.write( "a + 3c = 2d<BR>\n" );
document.write( "a + 3(3) = 2(8)<BR>\n" );
document.write( "a + 9 = 16<BR>\n" );
document.write( "a = 16 - 9<BR>\n" );
document.write( "a = 7<BR>\n" );
document.write( "and<BR>\n" );
document.write( "b = 2(3)<BR>\n" );
document.write( "b = 6<BR>\n" );
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document.write( "Our number: 7638<BR>\n" );
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document.write( "Check this using a + b + c + d = 3d<BR>\n" );
document.write( "7 + 6 + 3 + 8 = 3(8)<BR>\n" );
document.write( "24 = 24 </SPAN>\n" );
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