document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=515509>Question 515509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi..trying to help my son on his homework, and running into a bit of a wall on this one. I can intuit my way to the correct answer, but can't show how to get there algebraically.\r<BR>\n" );
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document.write( "\"Samantha invested her $10,000 savings at two different banks for one year. She put part of the money in Bank A which paid 8% interest. The rest of the money was invested at 7% at Bank B.At the end of the year she had accumulated $735 in interest. How much money did she invest at Bank A? Hint:7% interest on an unknown amount of money is .07n.\"\r<BR>\n" );
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document.write( "I can get the answer (6500$ at 7%, %3500 at 8%), but I can't see how to write out the equation. Any help you can provide would be greatly appreciated, as we've spent three hours on this assignment already! :)  Thank you again, we both greatly appreciate any time you give us!!!\r<BR>\n" );
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document.write( "-greg and gabe scott </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344010 by </B><A HREF=/tutors/aboutme.mpl?userid=drcole><B>drcole(72)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drcole><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=344010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the amount of money Samantha invested in Bank A, and let y be the amount she invested in Bank B.  The total amount of money she invested in the two banks was $10000, and we can represent this as an algebraic equation as:\r<BR>\n" );
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document.write( "x + y = 10000\r<BR>\n" );
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document.write( "Since Bank A paid 8% interest, she earned 0.08x in interest at Bank A.  Likewise, since Bank B paid 7% interest, she earned 0.07y at Bank B.  The total amount of interest she earned at the two banks was $735, and we can represent this fact as an algebraic equation as:\r<BR>\n" );
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document.write( "0.08x + 0.07y = 735\r<BR>\n" );
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document.write( "Now we have a system of two linear equations in two unknowns.  We can solve this system using the substitution method.  First, we will take the first equation and solve for x:\r<BR>\n" );
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document.write( "x + y = 10000<BR>\n" );
document.write( "x = 10000 - y (subtracting y from both sides)\r<BR>\n" );
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document.write( "Now we substitute 10000 - y for x in the second equation, yielding an equation involving y only:\r<BR>\n" );
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document.write( "0.08(10000 - y) + 0.07y = 735\r<BR>\n" );
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document.write( "Now we solve for y:\r<BR>\n" );
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document.write( "800 - 0.08y + 0.07y = 735 (distributing 0.08 in the left side)<BR>\n" );
document.write( "800 - 0.01y = 735 (combining like terms)<BR>\n" );
document.write( "-0.01y = -65 (subtracting 800 from both sides)<BR>\n" );
document.write( "y = 6500 (dividing both sides by -0.01)\r<BR>\n" );
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document.write( "So Samantha invested $6500 in Bank B, as you figured out intuitively.  Substituting 6500 back in for y in our equation for x, we then get:\r<BR>\n" );
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document.write( "x = 10000 - y = 10000 - 6500 = 3500\r<BR>\n" );
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document.write( "so, as you also figured out, she invested $3500 in Bank A. </SPAN>\n" );
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