document.write( "Question 44917: a small corporation borrowed $500,000 to expand its product line. Some of
\n" ); document.write( "the money was borrowed at 9%, some at 10% and some at 12%. How much was
\n" ); document.write( "borrowed at each rate if the annual interest was $52, 000 and the amount
\n" ); document.write( "borrowed at 10% was two and a half times the amount borrowed at 9%? \n" ); document.write( "

Algebra.Com's Answer #29788 by josmiceli(19441) $\"\"$ $\"About$

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x = amount borrowed at 9%
\n" ); document.write( "y = amount borrowed at 10%
\n" ); document.write( "z = amount borrowed at 12%
\n" ); document.write( " $\"x+%2B+y+%2B+z+=+500000\"$
\n" ); document.write( "Annual interest charged at 9% = $\".09%2Ax\"$
\n" ); document.write( "Annual interest charged at 10% = $\".10%2Ax\"$
\n" ); document.write( "Annual interest charged at 12% = $\".12%2Ax\"$
\n" ); document.write( "Total annual interest = 52000
\n" ); document.write( " $\".09%2Ax+%2B+.10%2Ay+%2B+.12%2Az+=+5.2+%2A+10%5E4\"$
\n" ); document.write( "according to problem, $\"y+=+2.5%2Ax\"$
\n" ); document.write( " $\".09%2Ax+%2B+.10%2A2.5%2Ax+%2B+.12%2Az+=+5.2+%2A+10%5E4\"$
\n" ); document.write( " $\".34%2Ax+%2B+.12%2Az+=+5.2+%2A+10%5E4\"$
\n" ); document.write( "also,
\n" ); document.write( " $\"x+%2B+y+%2B+z+=+500000\"$
\n" ); document.write( " $\"x+%2B+2.5%2Ax+%2B+z+=+50+%2A+10%5E4\"$
\n" ); document.write( " $\"3.5%2Ax+%2B+z+=+50+%2A+10%5E4\"$
\n" ); document.write( "multiply both sides of this equation by (-.12)
\n" ); document.write( " $\"-.42%2Ax+%2B+%28-.12%29%2Az+=+%28-.12%29%2A50+%2A+10%5E4\"$
\n" ); document.write( " $\"-.42%2Ax+-.12%2Az+=+-6+%2A+10%5E4\"$
\n" ); document.write( "and the other equation was
\n" ); document.write( " $\".34%2Ax+%2B+.12%2Az+=+5.2+%2A+10%5E4\"$
\n" ); document.write( "add these equations
\n" ); document.write( " $\"-.08%2Ax+=+-.8+%2A+10%5E4\"$
\n" ); document.write( "divide both sides by (-.08)
\n" ); document.write( " $\"x+=+10%2A10%5E4\"$
\n" ); document.write( " $\"x+=+100000\"$ amount borrowed at 9%
\n" ); document.write( " $\"y+=+2.5%2A100000\"$
\n" ); document.write( " $\"y+=+250000\"$ amount borrowed at 10%
\n" ); document.write( " $\"z+=+500000+-+350000+\"$
\n" ); document.write( " $\"z+=+150000\"$ amount borrowed at 12%
\n" ); document.write( "check
\n" ); document.write( " $\"3.5%2Ax+%2B+z+=+50+%2A+10%5E4\"$
\n" ); document.write( " $\"35%2A10%5E4+%2B+15%2A10%5E4+=+50+%2A+10%5E4\"$
\n" ); document.write( " $\"50%2A10%5E4+=+50%2A10%5E4\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );