document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160678>Question 160678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't understand how to set up this problem in order to solve it because the book examples do not break it up the same way.<BR>\n" );
document.write( "Dave invested half his money at 5%, one-third his money at 4%, and the rest of his money at 3.5%. If his total annual investment income was $530, how much had he invested? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118484 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=118484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first thing you have to do is find out what the rest is.<BR>\n" );
document.write( "several ways to do it.<BR>\n" );
document.write( "one way is as follows:<BR>\n" );
document.write( "1/2 + 1/3 + x = 1<BR>\n" );
document.write( "solve for x.<BR>\n" );
document.write( "easiest way is to multiply both sides of the equation by 6 to remove the denominators.<BR>\n" );
document.write( "equation becomes<BR>\n" );
document.write( "3 + 2 + 6*x = 6<BR>\n" );
document.write( "6*x = 6 - 3 - 2 = 1<BR>\n" );
document.write( "x = 1/6<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to see if that's correct, add up 1/2 + 1/3 + 1/6 to see if it adds up to 1.<BR>\n" );
document.write( "1/3 is the same as 2/6.<BR>\n" );
document.write( "1/2 is the same as 3/6<BR>\n" );
document.write( "so 2/6 + 3/6 + 1/6 = 6/6 = 1.<BR>\n" );
document.write( "x = 1/6 is good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you know what the total income each year is.<BR>\n" );
document.write( "it's $530.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "now you know that:<BR>\n" );
document.write( "1/2 of the money is invested at 5%.<BR>\n" );
document.write( "1/3 of the money is invested at 4%.<BR>\n" );
document.write( "1/6 of the money is invested at 3.5%<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if 1/2 of the money is invested at 5%, then the amount of income from 1/2 of the money at the end of the year is 5% times (1/2 of the money).<BR>\n" );
document.write( "this also means that 4% times (1/3 of the money) give you the amount of income from 1/3 of the money at the end of the year.<BR>\n" );
document.write( "this also means that 3.5% times (1/6) of the money) gives you the amount of income from 1/6 of the money<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let y = total amount of money invested.<BR>\n" );
document.write( "let $530 = total income from money invested.<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "5%*y*1/2 + 4%*y*1/3 + 3.5%*y*1/6 = $530<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this is the same as (5%*y)/2 + (4%*y)/3 + (3.5%*y)/6 = $530.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to get the interest rate you have to divide by 100%.  <BR>\n" );
document.write( "5% / 100% = .05<BR>\n" );
document.write( "4% / 100% = .04<BR>\n" );
document.write( "3.5% / 100% = .035<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you substitute interest rate for % interest and the equation becomes<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "(.05*y)/2 + (.04*y)/3 + (.035*y)/6 = $530.<BR>\n" );
document.write( "multiplying both sides of the equation by 6 to remove the denominators, and the equation becomes<BR>\n" );
document.write( "3*.05*y + 2*.04*y + .035*y = 6*$530<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( ".15*y + .08*y + .035*y = $3180<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( ".265*y = $3180<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "y = $3180/.265 which equals $12000.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove that the answer is correct, you substitute $12000 for y and solve the original equation after you converted from % to rate.<BR>\n" );
document.write( "that equation is .05*y*(1/2) + .04*y*(1/3) + .035*y*(1/6) = $530.<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( ".05*12000*(1/2) + .04*12000*(1/3) + .035*12000*(1/6) = $530.<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "$300 + $160 + $70 = $530<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "$530 = $530<BR>\n" );
document.write( "which proves the equation is good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your answer is total money invested is $12000.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );