document.write( "Question 1065392: Nico is saving money for his college education. He invests some money at 8%, and $1800 less than that amount at 6%, The investments produced a total of $270 interest in 1 year. How much did he invest at each rate? \n" ); document.write( "

Algebra.Com's Answer #680568 by josmiceli(19441) $\"\"$ $\"About$

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For simple interest, which this is
\n" ); document.write( " $\"+I+=+P%2Ar%2At+\"$
\n" ); document.write( " $\"+I+\"$ = interest earned over $\"+t+\"$ years
\n" ); document.write( " $\"+P+\"$ = amount invested
\n" ); document.write( " $\"+r+\"$ = rate of interest
\n" ); document.write( "---------------------------
\n" ); document.write( " $\"+t+=+1+\"$ yr
\n" ); document.write( "Let $\"+I%5B1%5D+\"$ = interest earned at 8%
\n" ); document.write( "Let $\"+I%5B2%5D+=+270+-+I%5B1%5D+\"$ = interest earned at 6%
\n" ); document.write( "Let $\"+P%5B1%5D+\"$ = amount invested at 8%
\n" ); document.write( " $\"+P%5B2%5D+=+P%5B1%5D+-+1800+\"$ = amount invested at 6%
\n" ); document.write( "----------------------------------------------
\n" ); document.write( " $\"+I%5B1%5D+=+P%5B1%5D%2A.08%2A1+\"$
\n" ); document.write( "(1) $\"+I%5B1%5D+=+.08P%5B1%5D+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+I%5B2%5D+=+P%5B2%5D%2A.06%2A1+\"$
\n" ); document.write( " $\"+270+-+I%5B1%5D+=+%28+P%5B1%5D+-+1800+%29%2A.06+\"$
\n" ); document.write( " $\"+270+-+I%5B1%5D+=+.06P%5B1%5D+-+108+\"$
\n" ); document.write( " $\"+.06P%5B1%5D+=+378+-+I%5B1%5D+\"$
\n" ); document.write( " $\"+P%5B1%5D+=+6300+-+%28+1%2F.06%29%2AI%5B1%5D+\"$
\n" ); document.write( "(2) $\"+P%5B1%5D+=+6300+-+%28+50%2F3+%29%2AI%5B1%5D+\"$
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+P%5B1%5D+=+6300+-+%28+50%2F3+%29%2A.08%2AP%5B1%5D+\"$
\n" ); document.write( "(2) $\"+P%5B1%5D+=+6300+-+%28+50%2F3+%29%2A%28+4%2F50+%29%2AP%5B1%5D+\"$
\n" ); document.write( "(2) $\"+P%5B1%5D+=+6300+-+%28+4%2F3+%29%2AP%5B1%5D+\"$
\n" ); document.write( "(2) $\"+%28+7%2F3+%29%2AP%5B1%5D+=+6300+\"$
\n" ); document.write( "(2) $\"+P%5B1%5D+=+%283%2F7%29%2A6300+\"$
\n" ); document.write( "(2) $\"+P%5B1%5D+=+2700+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+P%5B2%5D+=+P%5B1%5D+-+1800+\"$
\n" ); document.write( " $\"+P%5B2%5D+=+2700+-+1800+\"$
\n" ); document.write( " $\"+P%5B2%5D+=+900+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "He invested $2,700 @ 8%
\n" ); document.write( "He invested $900 @ 6%
\n" ); document.write( "--------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+I%5B1%5D+=+.08P%5B1%5D+\"$
\n" ); document.write( "(1) $\"+I%5B1%5D+=+.08%2A2700+\"$
\n" ); document.write( "(1) $\"+I%5B1%5D+=+216+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+I%5B2%5D+=+P%5B2%5D%2A.06+\"$
\n" ); document.write( "(2) $\"+I%5B2%5D+=+900%2A.06+\"$
\n" ); document.write( "(2) $\"+I%5B2%5D+=+54+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+I%5B1%5D+%2B+I%5B2%5D+=+216+%2B+54+\"$
\n" ); document.write( " $\"+I%5B1%5D+%2B+I%5B2%5D+=+270+\"$
\n" ); document.write( "OK\r
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