document.write( "Question 880545: Vanessa recently received a $75,000 inheritance. She distributed the money among three accounts bearing 6%, 8%, and 12% simple interest. The amount invested at 8% was three times that invested at 12%. If total interest after one year was $5,700, how much did she invest in each? \n" ); document.write( "

Algebra.Com's Answer #531547 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ = amt invested @ 6%
\n" ); document.write( "Let $\"+b+\"$ = amt invested @ 8%
\n" ); document.write( "Let $\"+c+\"$ = amt invested @ 12%
\n" ); document.write( "-------------------------------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+75000+\"$
\n" ); document.write( "(2) $\"+b+=+3c+\"$
\n" ); document.write( "(3) $\"+.06a+%2B+.08b+%2B+.12c+=+5700+\"$
\n" ); document.write( "--------------------------------------
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( "(1) $\"+a+%2B+3c+%2B+c+=+75000+\"$
\n" ); document.write( "(1) $\"+a+=+-4c+%2B+75000+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "Now substitute this result and (2) into (3)
\n" ); document.write( "(3) $\"+.06%2A%28+-4c+%2B+75000+%29+%2B+.08%2A%283c%29+%2B+.12c+=+5700+\"$
\n" ); document.write( "(3) $\"+-.24c+%2B+4500+%2B+.24c+%2B+.12c+=+5700+\"$
\n" ); document.write( "(3) $\"+.12c+=+1200+\"$
\n" ); document.write( "(3) $\"+c+=+10000+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(2) $\"+b+=+3c+\"$
\n" ); document.write( "(2) $\"+b+=+30000+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+75000+\"$
\n" ); document.write( "(1) $\"+a+%2B+30000+%2B+10000+=+75000+\"$
\n" ); document.write( "(1) $\"+a+=+75000+-+40000+\"$
\n" ); document.write( "(1) $\"+a+=+35000+\"$
\n" ); document.write( "amt invested @ 6% is $35,000
\n" ); document.write( "amt invested @ 8% is $30,000
\n" ); document.write( "amt invested @ 12% is $10,000
\n" ); document.write( "---------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+75000+\"$
\n" ); document.write( "(1) $\"+35000+%2B+30000+%2B+10000+=+75000+\"$
\n" ); document.write( "(1) $\"+75000+=+75000+\"$
\n" ); document.write( "OK
\n" ); document.write( "(3) $\"+.06a+%2B+.08b+%2B+.12c+=+5700+\"$
\n" ); document.write( "(3) $\"+.06%2A35000+%2B+.08%2A30000+%2B+.12%2A10000+=+5700+\"$
\n" ); document.write( "(3) $\"+2100+%2B+2400+%2B+1200+=+5700+\"$
\n" ); document.write( "(3) $\"+5700+=+5700+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );