document.write( "Question 1136030: Phyllis invested 43000dollars, a portion earning a simple interest rate of 5
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Algebra.Com's Answer #753776 by ikleyn(52810)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            I will show you two methods of solving this problem.\r
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\n" ); document.write( "\n" ); document.write( "Solution 1.   Using the system of 2 equations\r
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document.write( "Let  x  be the amount invested at 5% and  y  be the amount invested at 7%.\r\n" );
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document.write( "Then you have these two equations\r\n" );
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document.write( "    x   +     y = 43000   dollars     (1)    (the sum of amounts is equal to the total investment)\r\n" );
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document.write( "  0.05x + 0.07y =  2430   dollars     (2)    (the sum of interests is equal to the total interest)\r\n" );
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document.write( "I will apply the Substitution method to solve the system.\r\n" );
document.write( "For it, I express\r\n" );
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document.write( "    x = 43000 - y                     (3)\r\n" );
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document.write( "from the first equation and then substitute it into the second equation, replacing x. I will get\r\n" );
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document.write( "    0.05*(43000 - y) + 0.07y = 2430.  (4)\r\n" );
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document.write( "Simplify and solve this equation step by step:\r\n" );
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document.write( "    0.05*43000 - 0.05y + 0.07y = 2430\r\n" );
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document.write( "    0.07y - 0.05y = 2430 - 0.05*43000\r\n" );
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document.write( "    0.02y         = 280\r\n" );
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document.write( "        y         = \"280%2F0.02\" = 14000.\r\n" );
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document.write( "Thus we found that $14000 were invested at 7%.\r\n" );
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document.write( "To find x, use equation (3)\r\n" );
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document.write( "    x = 43000 - 14000 = 29000.\r\n" );
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document.write( "ANSWER.  $29000 invested at 5%  and  $14000 invested at 7%.\r\n" );
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document.write( "CHECK.   0.05*29000 + 0.07*14000 = 2430 dollars, the total interest.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 2.   Using single equation\r
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document.write( "Let  y  be the amount invested at 7%.\r\n" );
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document.write( "Then the amount invested at 5% is the rest  (43000-y) dollars.\r\n" );
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document.write( "The 5% investment gives the interest of  0.05*(43000-y)  dollars.\r\n" );
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document.write( "The 7% investment gives the interest of 0.07*y dollars.\r\n" );
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document.write( "In total, these two investments give $2430.  Therefore, the \"interest\" equation is\r\n" );
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document.write( "    0.05*(43000-y) + 0.07*y = 2430.\r\n" );
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document.write( "It is the same equation (4) as you obtained in the Solution 1  after substitution.\r\n" );
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document.write( "So, the solution of this equation is the same, and it produces the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "You learned two methods setuping the equations along with the methods of their solutions.\r
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\n" ); document.write( "\n" ); document.write( "It is a standard and typical problem on investments.\r
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\n" ); document.write( "\n" ); document.write( "If you need more details,  or if you want to see other similar problems solved by different methods,  look into the lesson \r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on investment\r
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\n" ); document.write( "\n" ); document.write( "You will find there different approaches  (using one equation or a system of two equations in two unknowns),  as well as
\n" ); document.write( "different methods of solution to the equations  (Substitution,  Elimination).\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic  \"Systems of two linear equations in two unknowns\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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