document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035904>Question 1035904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This question was in my daughters Year 8 maths test today and I am of no help\r<BR>\n" );
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document.write( "A father observes that the ratio of his age to his daughters age is 3:2 right now. But his daughter observes that in 8 years time their ages will be 7:5<BR>\n" );
document.write( "Is this enough information to determine their ages?<BR>\n" );
document.write( "If Yes, what are their ages<BR>\n" );
document.write( "If No, explain why\r<BR>\n" );
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document.write( "Thanks for your help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650512 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=650512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Grade 8 level exercise, not sure.  Variables would be helpful.\r<BR>\n" );
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document.write( "y for Father's age now.<BR>\n" );
document.write( "x for daughter's age now.\r<BR>\n" );
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document.write( "Transcribe or translate the description, literally.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28system%28y%2Fx=3%2F2%2C%28y%2B8%29%2F%28x%2B8%29=7%2F5%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28system%28y%2Fx=3%2F2%2C%28y%2B8%29%2F%28x%2B8%29=7%2F5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is a system of two of what really are LINEAR equations in two unknown variables.<BR>\n" );
document.write( "If your daughter is in a Pre-Algebra course, maybe she will understand this discussion just<BR>\n" );
document.write( "given, and could solve the system of equations. \r<BR>\n" );
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document.write( "---<BR>\n" );
document.write( "REVIEWING WHAT WAS JUST POSTED:\r<BR>\n" );
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document.write( "(1)<BR>\n" );
document.write( "Assigned variables for the current ages of Father and his Daughter\r<BR>\n" );
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document.write( "(2)<BR>\n" );
document.write( "Translated the description of the problem into equations\r<BR>\n" );
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document.write( "(3)<BR>\n" );
document.write( "Need to SOLVE the system of equations  (not yet shown)\r<BR>\n" );
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document.write( "You want to solve the system of equations and to know if in fact, the system <i>can</i> be solved.  Let us try some arithmetic or algebra steps.\r<BR>\n" );
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document.write( "Try using multiplicative inverse property.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%28y%2Fx%29=x%283%2F2%29%2C%285%28x%2B8%29%29%28%28y%2B8%29%2F%28x%2B8%29%29=%285%28x%2B8%29%29%287%2F5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=3x%2F2%2C5%28y%2B8%29=%28x%2B8%29%2A7%29 ALIGN=MIDDLE  ALT=\"system%28y=3x%2F2%2C5%28y%2B8%29=%28x%2B8%29%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify the second equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=3x%2F2%2C5y%2B40=7x%2B56%29 ALIGN=MIDDLE  ALT=\"system%28y=3x%2F2%2C5y%2B40=7x%2B56%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute for y into the second equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%283x%2F2%29%2B40=7x%2B56 ALIGN=MIDDLE  ALT=\"5%283x%2F2%29%2B40=7x%2B56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "continue algebraic steps, not saying the names of the properties being used (hopefully they are not needed to be identified...)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%2F2%2B40=7x%2B56 ALIGN=MIDDLE  ALT=\"15x%2F2%2B40=7x%2B56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%2B80=14x%2B112 ALIGN=MIDDLE  ALT=\"15x%2B80=14x%2B112\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x-14x%2B80=112 ALIGN=MIDDLE  ALT=\"15x-14x%2B80=112\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B80=112 ALIGN=MIDDLE  ALT=\"x%2B80=112\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=112-80 ALIGN=MIDDLE  ALT=\"x=112-80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=32%29 ALIGN=MIDDLE  ALT=\"highlight%28x=32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--------one of the results, the daughter's age now.\r<BR>\n" );
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document.write( "Use the first equation found before the system was simplified, being y=3x/2 and evaluate y, knowing the found value for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2832%29%2F2 ALIGN=MIDDLE  ALT=\"y=3%2832%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2A32%29%2F2 ALIGN=MIDDLE  ALT=\"y=%283%2A32%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2A2%2A16%29%2F2 ALIGN=MIDDLE  ALT=\"y=%283%2A2%2A16%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2A16 ALIGN=MIDDLE  ALT=\"y=3%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=48%29 ALIGN=MIDDLE  ALT=\"highlight%28y=48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------------result for father's age now. </SPAN>\n" );
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