document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168836>Question 168836</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013133798x/algebrahomeworkh>Prentice Hall Algebra 2 with Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: \r<BR>\n" );
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document.write( "numeric word problem using 3 equations.\r<BR>\n" );
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document.write( "The sum of three number is 105. The third is 11 less than 10 times the second. Twice the first is 7 more than three times the second. Find the Numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124492 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=124492\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = first number.<BR>\n" );
document.write( "let b = second number.<BR>\n" );
document.write( "let c = third number.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "sum of 3 numbers is 105<BR>\n" );
document.write( "a + b + c = 105<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "third number is 11 less than 10 times the second.<BR>\n" );
document.write( "c = 10*b - 11<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "twice the first number is 7 more than 3 times the second.<BR>\n" );
document.write( "2*a = 3*b + 7<BR>\n" );
document.write( "a = (3*b+7)/2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "start with:<BR>\n" );
document.write( "a + b + c = 105<BR>\n" );
document.write( "substitute for a:<BR>\n" );
document.write( "(3*b+7)/2 + b + c = 105<BR>\n" );
document.write( "substitute for c:\"<BR>\n" );
document.write( "(3*b+7)/2 + b + 10*b - 11 = 105<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "equation is now in terms of b and can be solved.<BR>\n" );
document.write( "expand all terms by removing parentheses:<BR>\n" );
document.write( "3*b/2 + 7/2 + b + 10*b - 11 = 105<BR>\n" );
document.write( "multiply both sides of equation by 2:<BR>\n" );
document.write( "3*b + 7 + 2*b + 20*b - 22 = 210<BR>\n" );
document.write( "combine like terms:<BR>\n" );
document.write( "25*b - 15 = 210<BR>\n" );
document.write( "add 15 to both sides of equation:<BR>\n" );
document.write( "25*b = 225<BR>\n" );
document.write( "divide both sides of equation by 25:<BR>\n" );
document.write( "b = 9<BR>\n" );
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document.write( "if b = 9, then:<BR>\n" );
document.write( "(3*b+7)/2 = (27+7)/2 = 34/2 = 17 = a<BR>\n" );
document.write( "and:<BR>\n" );
document.write( "10*b - 11 = 90 - 11 = 79 = c<BR>\n" );
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document.write( "you have:<BR>\n" );
document.write( "a = 17<BR>\n" );
document.write( "b = 9<BR>\n" );
document.write( "c = 79<BR>\n" );
document.write( "total = 105<BR>\n" );
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document.write( "total = a + b + c = 79 + 9 + 17 = 88 + 17 = 105 (ok)<BR>\n" );
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document.write( "c = 10*b - 11 becomes:<BR>\n" );
document.write( "c = 10*9 - 11 = 90 - 11 = 79 (ok) <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a = (3*b+7)/2 becomes:<BR>\n" );
document.write( "a = (3*9+7)/2 = (27+7)/2 = 35/2 = 17 (ok)<BR>\n" );
document.write( "-----\r<BR>\n" );
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document.write( " </SPAN>\n" );
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