document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=402002>Question 402002</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A is eleven times as old as B. In a certain number of years A will be five times as old as B, and five years after that she will be three times as old as B. How old are they now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #284421 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=284421\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation for each statement, simplify each equation:<BR>\n" );
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document.write( "\"A is eleven times as old as B.\"<BR>\n" );
document.write( "a = 11b<BR>\n" );
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document.write( "\"In a certain number of years A will be five times as old as B,\"; y = no. of yrs<BR>\n" );
document.write( "a + y = 5(b+y)<BR>\n" );
document.write( "a + y = 5b + 5y<BR>\n" );
document.write( "a = 5b + 5y - y<BR>\n" );
document.write( "a = 5b + 4y<BR>\n" );
document.write( "replace a with 11b<BR>\n" );
document.write( "11b = 5b + 4y<BR>\n" );
document.write( "11b - 5b = 4y<BR>\n" );
document.write( "6b = 4y<BR>\n" );
document.write( "6b - 4y = 0<BR>\n" );
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document.write( "\"five years after that she will be three times as old as B.\" That's y+5 yrs<BR>\n" );
document.write( "a + y + 5 = 3(b + y + 5)<BR>\n" );
document.write( "a + y + 5 = 3b + 3y + 15<BR>\n" );
document.write( "a = 3b + 3y - y + 15 - 5<BR>\n" );
document.write( "a = 3b + 2y + 10<BR>\n" );
document.write( "replace a with 11b<BR>\n" );
document.write( "11b = 3b + 2y + 10<BR>\n" );
document.write( "11b - 3b = 2y + 10<BR>\n" );
document.write( "8b = 2y + 10<BR>\n" );
document.write( "8b - 2y = 10<BR>\n" );
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document.write( "Multiply above equation by -2, add to the 1st equation<BR>\n" );
document.write( "-16b + 4y = -20<BR>\n" );
document.write( " 6b - 4y = 0<BR>\n" );
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document.write( "-10b = -20<BR>\n" );
document.write( "b = 2 yrs old<BR>\n" );
document.write( "Find a<BR>\n" );
document.write( "a = 11(2)<BR>\n" );
document.write( "a = 22 yrs old<BR>\n" );
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document.write( "We can say their present ages are: A=22; B=2<BR>\n" );
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document.write( "To check our our solutions, Find y<BR>\n" );
document.write( "6(2) - 4y = 0<BR>\n" );
document.write( "12 - 4y = 0<BR>\n" );
document.write( "-4y = -12<BR>\n" );
document.write( "y = 3 yrs is that \"certain number of years\"<BR>\n" );
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document.write( "Check in the statement:<BR>\n" );
document.write( "\"In a certain number of years A will be five times as old as B,<BR>\n" );
document.write( "22 + 3 = 5(2 + 3)<BR>\n" );
document.write( "25 = 25<BR>\n" );
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document.write( "You can check the solutions in the 3rd statement:<BR>\n" );
document.write( "\"five years after that she will be three times as old as B.\" That's y+5 yrs\"\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );