document.write( "Question 1142733: A college used a $7,000 gift from an alumnus to make two student loans. The first was at 3% annual interest to a nursing student. The second was at 6% to a business major. If the college collected $300 in interest the first year, how much was loaned to each student? \n" ); document.write( "

Algebra.Com's Answer #763459 by ikleyn(52782) $\"\"$ $\"About$

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document.write( "Let x = the amount loaned at 6% and y = the amount loaned at 3%.\r\n" );
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document.write( "Then from the condition you have these two equations in two unknowns\r\n" );
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document.write( "        x +     y = 7000  dollars      (1)    (total of the two loans)\r\n" );
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document.write( "    0.06x + 0.03y =  300  dollars      (2)    (total interest)\r\n" );
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document.write( "Solve the system by the Substitution method.\r\n" );
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document.write( "For it, from equation (1) express x = 7000 - y  and substitute it into equation (2). You will get\r\n" );
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document.write( "    0.06*(7000-y) + 0.03y = 300\r\n" );
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document.write( "Simplify and express y from the last equation; then calculate\r\n" );
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document.write( "    y =  = 4000.\r\n" );
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document.write( "To find x, substitute the found value of y into equation (1). You will get then\r\n" );
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document.write( "    x = 7000 - 4000 = 3000.\r\n" );
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document.write( "ANSWER.  $4000 was loaned at  3%  and  $3000 was loaned at 6%.\r\n" );
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document.write( "CHECK.   0.03*4000 + 0.6*3000 = 300  dollars.    ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a typical and standard problem on investment.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems on investment, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Using systems of equations to solve problems on investment\r
\n" ); document.write( "\n" ); document.write( "in this site.\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
\n" ); document.write( "
\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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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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