document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200212>Question 1200212</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Recall captain hook's riddle from the beginning of chapter 4: \r<BR>\n" );
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document.write( "ye have almost found the treasure. start from this spot and walk north and east. three times the sum of the number of northerly steps and the number of the easterly steps is four more than four times the number of northerly steps. more than this you will need to find the treasure. ye also must know that when ye multiply by five the number two less than the number of northerly steps, ye get the number that is two more than seven times the number of easterly steps. \r<BR>\n" );
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document.write( "How many steps north and east should you take to get to the treasure?<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 #834288 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=834288\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The first task is to translate each verbal sentence into symbolic algebraic equations.\r<BR>\n" );
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document.write( "Focus on the first sentence:<BR>\n" );
document.write( "\"three times the sum of the number of northerly steps and the number of the easterly steps is four more than four times the number of northerly steps.\"\r<BR>\n" );
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document.write( "More specifically, we'll translate the portion highlighted in blue<BR>\n" );
document.write( "\"<font color=blue>three times the sum of the number of northerly steps and the number of the easterly steps</font> is four more than four times the number of northerly steps.\"\r<BR>\n" );
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document.write( "x = number of steps going north<BR>\n" );
document.write( "y = number of steps going east<BR>\n" );
document.write( "x+y = the sum of those items<BR>\n" );
document.write( "3(x+y) = three times that sum<BR>\n" );
document.write( "Let's call this expression A. We'll use this later.\r<BR>\n" );
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document.write( "Now focus on this portion highlighted in blue<BR>\n" );
document.write( "\"three times the sum of the number of northerly steps and the number of the easterly steps is <font color=blue>four more than four times the number of northerly steps</font>.\"\r<BR>\n" );
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document.write( "x = number of steps going north<BR>\n" );
document.write( "4x = four times the number of steps going north<BR>\n" );
document.write( "4x+4 = four more compared to the previous quantity<BR>\n" );
document.write( "Let's call this expression B.\r<BR>\n" );
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document.write( "Expressions A and B are set equal to each other because of the key term \"is\" in the sentence \"three times the sum of the number of northerly steps and the number of the easterly steps <u><font color=red size=4>is</font></u> four more than four times the number of northerly steps\"<BR>\n" );
document.write( "It's like saying \"x is 10\" which translates to x = 10.\r<BR>\n" );
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document.write( "Equating those expressions gives us this equation<BR>\n" );
document.write( "3(x+y) = 4x+4\r<BR>\n" );
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document.write( "The next sentence to tackle is:<BR>\n" );
document.write( "\"ye also must know that when ye multiply by five the number two less than the number of northerly steps, ye get the number that is two more than seven times the number of easterly steps.\"\r<BR>\n" );
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document.write( "Let's narrow our focus to the stuff in blue<BR>\n" );
document.write( "\"<font color=blue>ye also must know that when ye multiply by five the number two less than the number of northerly steps</font>, ye get the number that is two more than seven times the number of easterly steps.\"\r<BR>\n" );
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document.write( "x = number of northerly steps<BR>\n" );
document.write( "x-2 = two fewer steps compared to before<BR>\n" );
document.write( "5(x-2) = five times the previous quantity<BR>\n" );
document.write( "Call this expression C.\r<BR>\n" );
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document.write( "Change the focus to this portion<BR>\n" );
document.write( "\"ye also must know that when ye multiply by five the number two less than the number of northerly steps, ye get the number that is <font color=blue>two more than seven times the number of easterly steps</font>.\"\r<BR>\n" );
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document.write( "y = number of easterly steps<BR>\n" );
document.write( "7y = seven times the previous amount<BR>\n" );
document.write( "7y+2 = two more than the previous quantity<BR>\n" );
document.write( "Call this expression D.\r<BR>\n" );
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document.write( "The expressions C and D are set equal to one another for similar reasoning compared to before.<BR>\n" );
document.write( "C = D<BR>\n" );
document.write( "5(x-2) = 7y+2\r<BR>\n" );
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document.write( "The key takeaways is what we have this system of equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%0D%0A3%28x%2By%29+=+4x%2B4%2C%0D%0A5%28x-2%29+=+7y%2B2%0D%0A%29%0D%0A ALIGN=MIDDLE  ALT=\"system%28%0D%0A3%28x%2By%29+=+4x%2B4%2C%0D%0A5%28x-2%29+=+7y%2B2%0D%0A%29%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's solve the 2nd equation for x.<BR>\n" );
document.write( "5(x-2) = 7y+2<BR>\n" );
document.write( "5x-10 = 7y+2<BR>\n" );
document.write( "5x = 7y+2+10<BR>\n" );
document.write( "5x = 7y+12<BR>\n" );
document.write( "x = (7y+12)/5<BR>\n" );
document.write( "x = (7y/5)+(12/5)<BR>\n" );
document.write( "x = 1.4y + 2.4\r<BR>\n" );
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document.write( "Then we'll substitute that into the other equation to solve for y.<BR>\n" );
document.write( "3(x+y) = 4x+4<BR>\n" );
document.write( "3(1.4y + 2.4+y) = 4(1.4y + 2.4)+4<BR>\n" );
document.write( "3(2.4y + 2.4) = 4(1.4y + 2.4)+4<BR>\n" );
document.write( "7.2y + 7.2 = 5.6y + 9.6+4<BR>\n" );
document.write( "7.2y + 7.2 = 5.6y + 13.6<BR>\n" );
document.write( "7.2y-5.6y = 13.6 - 7.2<BR>\n" );
document.write( "1.6y = 6.4<BR>\n" );
document.write( "y = (6.4)/(1.6)<BR>\n" );
document.write( "y = 4\r<BR>\n" );
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document.write( "Now we can determine x.<BR>\n" );
document.write( "x = 1.4y + 2.4<BR>\n" );
document.write( "x = 1.4*4 + 2.4<BR>\n" );
document.write( "x = 5.6 + 2.4<BR>\n" );
document.write( "x = 8\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "We found that<BR>\n" );
document.write( "x = 8<BR>\n" );
document.write( "y = 4\r<BR>\n" );
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document.write( "It tells us to go 8 steps north and 4 steps east.<BR>\n" );
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