document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=707181>Question 707181</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Caroline Case won $60,000 on a slot machine in Las Vegas.  She invested part of the money at 2% simple interest and the rest at 3%.  In one year, she earned a total of $1600 in interest.  How much was invested at the 3% rate?\r<BR>\n" );
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document.write( "Please explain step by step how to solve thiS! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #435614 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=435614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = amount invested at 2%, y = amount invested at 3%\r<BR>\n" );
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document.write( "She invested $60,000 total, so\r<BR>\n" );
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document.write( "x+y = 60000\r<BR>\n" );
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document.write( "solve for y to get:  y = 60000 - x\r<BR>\n" );
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document.write( "If she invests x dollars at 2% interest, then she will earn 0.02x dollars in interest alone after one year. Similarly, she will earn 0.03y dollars if she invests y dollars at 3%\r<BR>\n" );
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document.write( "In total, she will earn 0.02x + 0.03y dollars in interest alone from both accounts combined.\r<BR>\n" );
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document.write( "We're told that \"In one year, she earned a total of $1600 in interest\", so \r<BR>\n" );
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document.write( "Total Interest Earned = 1600\r<BR>\n" );
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document.write( "0.02x + 0.03y = 1600\r<BR>\n" );
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document.write( "Now plug in  y = 60000 - x and solve for x\r<BR>\n" );
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document.write( "0.02x + 0.03y = 1600\r<BR>\n" );
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document.write( "0.02x + 0.03(60000 - x) = 1600\r<BR>\n" );
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document.write( "0.02x + 0.03(60000) - 0.03x = 1600\r<BR>\n" );
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document.write( "0.02x + 1800 - 0.03x = 1600\r<BR>\n" );
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document.write( "-0.01x + 1800 = 1600\r<BR>\n" );
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document.write( "-0.01x = 1600 - 1800\r<BR>\n" );
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document.write( "-0.01x = -200\r<BR>\n" );
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document.write( "x = -200/(-0.01)\r<BR>\n" );
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document.write( "x = 20000\r<BR>\n" );
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document.write( "So $20,000 was invested at 2% simple interest\r<BR>\n" );
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document.write( "y = 60000 - x\r<BR>\n" );
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document.write( "y = 60000 - 20000\r<BR>\n" );
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document.write( "y = 40000\r<BR>\n" );
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document.write( "and $40,000 was invested at 3% simple interest\r<BR>\n" );
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document.write( "Check: \r<BR>\n" );
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document.write( "we can see that the two amounts $20,000 and $40,000 add to $60,000, so that checks out\r<BR>\n" );
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document.write( "$20,000 invested at 2% gives you 20000*0.02*1 = 400 dollars in interest alone\r<BR>\n" );
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document.write( "$40,000 invested at 3% gives you 40000*0.03*1 = 1200 dollars in interest alone\r<BR>\n" );
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document.write( "In total, you get 400+1200 = 1600 dollars in interest alone\r<BR>\n" );
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document.write( "So the answers are verified. </SPAN>\n" );
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