document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246287>Question 246287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you could please show me the formula, I think I could solve it myself. A teacher has the choice of two investment plans, one at 11% and the other at 13%. If the same amount invested at 13% yields 150.00 more per year, how much does she have to invest? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179896 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179896\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would assume you could possibly solve this as follows:\r<BR>\n" );
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document.write( "Let x = the amount she has to invest.\r<BR>\n" );
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document.write( "x * 1.11 = y\r<BR>\n" );
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document.write( "x * 1.13 = y + 150\r<BR>\n" );
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document.write( "You can solve for x or y in each equation.\r<BR>\n" );
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document.write( "This would be your choice.\r<BR>\n" );
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document.write( "I'll solve for x in terms of y first.\r<BR>\n" );
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document.write( "Then I'll make those equations equal to each other and then solve for y.\r<BR>\n" );
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document.write( "Once I've solved for y, I'll then go back in and solve for x.\r<BR>\n" );
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document.write( "IF YOU JUST WANT THE EQUATIONS THEN YOU CAN STOP HERE AND SOLVE IT YOURSELF.\r<BR>\n" );
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document.write( "I SOLVED IT DOWN BELOW.   YOU CAN USE THAT FOR REFERENCE IF YOU WISH.\r<BR>\n" );
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document.write( "Your first equation is x * 1.11 = y\r<BR>\n" );
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document.write( "divide both sides of this equation by 1.11 to get x = y/1.11\r<BR>\n" );
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document.write( "Your second equation is x * 1.13 = y + 150\r<BR>\n" );
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document.write( "divide both sides of this equation by 1.13 to get x = (y+150)/1.13\r<BR>\n" );
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document.write( "You now have two equations, both equal to x.\r<BR>\n" );
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document.write( "You have:\r<BR>\n" );
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document.write( "x = y/1.11 and x = (y+150)/1.13\r<BR>\n" );
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document.write( "Since they both equal to x, then they both equal to each other so you get:\r<BR>\n" );
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document.write( "y/1.11 = (y+150)/1.13\r<BR>\n" );
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document.write( "multiply both sides of the equation by (1.11)*(1.13) to get:\r<BR>\n" );
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document.write( "1.13*y = 1.11*(y+150)\r<BR>\n" );
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document.write( "simplify by removing parentheses to get:\r<BR>\n" );
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document.write( "1.13*y = 1.11*y + 1.11*150\r<BR>\n" );
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document.write( "subtract 1.11*y from both sides of equation to get:\r<BR>\n" );
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document.write( "1.13*y - 1.11*y = 1.11*150\r<BR>\n" );
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document.write( "simplify further by combining like terms and performing indicated operations to get:\r<BR>\n" );
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document.write( ".02*y = 166.5\r<BR>\n" );
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document.write( "divide both sides of equation by .02 to get:\r<BR>\n" );
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document.write( "y = 166.5/.02 = 8325\r<BR>\n" );
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document.write( "now that you know y, you can solve for x.\r<BR>\n" );
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document.write( "your first equation is 1.11 * x = y\r<BR>\n" );
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document.write( "this means that x = 8325/1.11 = 7500\r<BR>\n" );
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document.write( "your second equation is 1.13 * x = y + 150\r<BR>\n" );
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document.write( "this becomes 1.13 * x = 8475\r<BR>\n" );
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document.write( "this means that x = 8475 / 1.13 = 7500\r<BR>\n" );
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document.write( "x is equal to 7500 in both equations, so the value for y is good.\r<BR>\n" );
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document.write( "substitute for x in your original equations to get:\r<BR>\n" );
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document.write( "1.11 * x = 8325<BR>\n" );
document.write( "1.13 * x = 8475\r<BR>\n" );
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document.write( "8475 - 8325 = 150 so we're good all around.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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