document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74156>Question 74156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Joe Student wins the lottery!  Being a loyal Northwesterner he decides to invest his $13,000 in local companies.  He invests part of the principal in Starbuck's stock which gains 7% in value and, sadly, the rest of his winnings on Boeing stock which loses 10% of it's value in one year.  At the end of the year Joe's stock has gained $60 in value.  How much did he invest in each company?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53189 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=53189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call Joe's investment in Starbuck's S and Joe's investment in Boeing B. Since we know the two<BR>\n" );
document.write( "investments total $13,000 we can write the equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "S + B = 13000<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We also know that Joe's investment in Starbuck's gains 7% in value and his investment in<BR>\n" );
document.write( "Boeing loses 10% and if we total the two investments the answer is $60.  Using decimals for<BR>\n" );
document.write( "percents this becomes in equation form:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "0.07S - 0.10B = 60<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply this equation (all terms) by 100 to eliminate the decimals and get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "7S - 10B = 6000<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Return to our first equation and solve it for one of the variables in terms of the other.<BR>\n" );
document.write( "For example, solve for S by subtracting B from both sides to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "S = 13000 - B<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute the right side of this equation for S into the return equation as follows:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "7S - 10B = 6000<BR>\n" );
document.write( ".<BR>\n" );
document.write( "7(13000 - B) - 10B = 6000<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply out to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "91000 - 7B - 10B = 6000<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Combine the two terms containing B<BR>\n" );
document.write( ".<BR>\n" );
document.write( "91000 - 17B = 6000<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the 91000 on the left side by subtracting 91000 from both sides to obtain:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-17B = -85,000<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Divide both sides by -17 to find B<BR>\n" );
document.write( ".<BR>\n" );
document.write( "B = (-85000/-17) = 5000<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So we know that Joe had $5,000 invested in Boeing Stock.  Since he invested $13,000 total<BR>\n" );
document.write( "the remaining $8,000 was invested in Starbuck's.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand this problem and the need for two separate equations<BR>\n" );
document.write( "to solve for the two variables. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );