document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166784>Question 1166784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Beethoven started to compose music at a very young age. Bur Mozart was even <BR>\n" );
document.write( "    younger when he started. The sum of their ages at that time was 17. The difference  <BR>\n" );
document.write( "    was 7. How old was each when they started composing?<BR>\n" );
document.write( "     Answer here: (note: you may use GUESS and TEST)<BR>\n" );
document.write( "	A. Read and Understand:<BR>\n" );
document.write( "		What do you want to find? <BR>\n" );
document.write( "		<BR>\n" );
document.write( "		B. Devise a PLAN<BR>\n" );
document.write( "		What is your plan?<BR>\n" );
document.write( "    C.   Implement the PLAN<BR>\n" );
document.write( "		What is the solution and answer?<BR>\n" );
document.write( "    D. Look BACK/Check<BR>\n" );
document.write( "		Is the sum of the ages equal to 17?<BR>\n" );
document.write( "		Is the difference of the ages equal to 7?<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 #791323 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53937)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791323\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "The given post offers me unexpected and interesting disposition.\r<BR>\n" );
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document.write( "From one side, it is targeted to children who are related to music by some way and know the names of Beethoven and Mozart.\r<BR>\n" );
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document.write( "From the other side, as it is clear from the context, the assignment is targeted to young students who are not experienced in Algebra.\r<BR>\n" );
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document.write( "Before developing further my observations, let me notice that both Algebra and music have a lot in common: they both teach students and people <BR>\n" );
document.write( "in general  to feel a harmony.\r<BR>\n" );
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document.write( "So, we have an Algebra problem offered to young students, who are related to music and are not experienced in Algebra.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Now the question is: &nbsp;can I teach such students to solve the posed problem ? \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- can I teach them to something useful ?\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- can I present my teaching in a way that they will understand me ?  <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- and can &nbsp;I, &nbsp;at last, &nbsp;to make my teaching attractive for them just from the first minute?\r<BR>\n" );
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document.write( "The answer is &nbsp;&nbsp;\"YES, &nbsp;I &nbsp;can\".\r<BR>\n" );
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document.write( "The strategy of solution to the problem is as follows.\r<BR>\n" );
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document.write( "You are given that the sum of their ages is 17, while the difference of their ages is 7.\r\n" );
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document.write( "    1)  Take the middle point between 7 and 17.  It is 12, obviously. (Same as half the sum).\r\n" );
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document.write( "    2)  This middle value is nothing else as the age of the older person (Beethoven, in this case,\r\n" );
document.write( "             since we know that Beethoven was older than Mozart when started learning music).\r\n" );
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document.write( "    3)  Next subtract the given difference of ages 7 from the Bethowen age  12 - 7 = 5.\r\n" );
document.write( "        It is the age of Mozart when he started.\r\n" );
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document.write( "    5)  So the ages were 5 years for Mozart and 12 years for Beethoven.   It is the <U>ANSWER</U> to the problem.\r\n" );
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document.write( "Solved.   //  Which means that the solution is completed.\r\n" );
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document.write( "Now, similar to as the composers check their writing by playing it, in Algebra we check our answers by substituting them into the problem' condition.\r\n" );
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document.write( "By doing it, we see that the sum of 12 and 5 is 17, and the difference of 12 and 5 is 7 - same as stated in the problem.\r\n" );
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document.write( "So the problem is solved and checked.\r\n" );
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document.write( "And then I'd complete my performance as a teacher by saying to my students that the method I tought them is a GENERAL method,\r\n" );
document.write( "which works ALWAYS in solving similar problems.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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