document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466550>Question 466550</A>: <I><SPAN STYLE=\"word-break: break-all;\"> heather is twice as old as armida while kaye is 35 years youner than heather. if 1/2 the age ofarmida  5 years ago , and  1/3 of the age of heathr  10 years from now  is twice the age of kaye, how old is kaye now?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319895 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=319895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Heather is twice as old as Armida while Kaye is 35 years younger than Heather.<BR>\n" );
document.write( "If 1/2 the age of Armida 5 years ago, and 1/3 of the age of Heather 10 years from now, is twice the age of Kaye, how old is Kaye.<BR>\n" );
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document.write( "Let h = Heather's present age<BR>\n" );
document.write( "Let a = Armida's<BR>\n" );
document.write( "Let k = Kaye's <BR>\n" );
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document.write( "Write an equation for each statement:<BR>\n" );
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document.write( "\"Heather is twice as old as Armida\"<BR>\n" );
document.write( "h = 2a<BR>\n" );
document.write( "or<BR>\n" );
document.write( "a = .5h<BR>\n" );
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document.write( "\"while Kaye is 35 years younger than Heather.\"<BR>\n" );
document.write( "k = h - 35<BR>\n" );
document.write( "or<BR>\n" );
document.write( "h = (k+35)<BR>\n" );
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document.write( "we need to get a in terms of k also<BR>\n" );
document.write( "a = .5(k+35)<BR>\n" );
document.write( "a = (.5k+17.5)<BR>\n" );
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document.write( "\"If 1/2 the age of Armida 5 years ago, and 1/3 of the age of Heather 10 years from now, is twice the age of Kaye,\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(a-5) + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(h+10) = 2k<BR>\n" );
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document.write( "multiply by 6 to clear the denominators, results:<BR>\n" );
document.write( "3(a-5) + 2(h+10) = 6(2k)<BR>\n" );
document.write( "3a - 15 + 2h + 20 = 12k<BR>\n" );
document.write( "3a + 2h + 5 = 12k<BR>\n" );
document.write( "replace h with 2a<BR>\n" );
document.write( "3a + 2(2a) + 5 = 12k<BR>\n" );
document.write( "3a + 4a + 5 = 12k<BR>\n" );
document.write( "7a + 5 = 12k<BR>\n" );
document.write( "Replace a with (.5k+17.5))<BR>\n" );
document.write( "7(.5k+17.5) + 5 = 12k<BR>\n" );
document.write( "3.5k + 122.5 + 5 = 12k<BR>\n" );
document.write( "3.5k + 127.5 = 12k<BR>\n" );
document.write( "127.5 = 12k - 3.5k<BR>\n" );
document.write( "127.5 = 8.5k<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=127.5%2F8.5 ALIGN=MIDDLE  ALT=\"127.5%2F8.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "k = 15 yrs is Kaye's age<BR>\n" );
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document.write( "A lot of chances to make a mistake here, check this:<BR>\n" );
document.write( "h = 15 + 35 = 50<BR>\n" );
document.write( "a = .5(50) = 25 <BR>\n" );
document.write( "Use these values in the statement:<BR>\n" );
document.write( "\"If 1/2 the age of Armida 5 years ago, and 1/3 of the age of Heather 10 years from now, is twice the age of Kaye,\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(25-5) + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(50+10) = 2(15)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(20) + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(60) = 30<BR>\n" );
document.write( "10 + 20 = 30; confirms are solution\r<BR>\n" );
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