document.write( "Question 1066863: A man has two investments, one paying 5% annual interest and the other at 8%. The total annual income from the two investments is P 4,650. If the interest rates were interchanged, the total annual income would be P 5,100. Find the amount invested. of each rate. \n" ); document.write( "

Algebra.Com's Answer #682092 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2At+\"$
\n" ); document.write( "(1) $\"+I%5B1%5D+=+P%5B1%5D%2A.05%2A1+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( " $\"+I%5B2%5D+=+P%5B2%5D%2Ar%5B2%5D%2At+\"$
\n" ); document.write( "(2) $\"+I%5B2%5D+=+P%5B2%5D%2A.08%2A1+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "(3) $\"+I%5B1%5D+%2B+I%5B2%5D+=+4650+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "Now just swap the interest rates
\n" ); document.write( " $\"+I%5B1%5D+=+P%5B1%5D%2Ar%5B2%5D%2At+\"$
\n" ); document.write( "(4) $\"+I%5B3%5D+=+P%5B1%5D%2A.08%2A1+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( " $\"+I%5B2%5D+=+P%5B2%5D%2Ar%5B1%5D%2At+\"$
\n" ); document.write( "(5) $\"+I%5B4%5D+=+P%5B2%5D%2A.05%2A1+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "(6) $\"+I%5B3%5D+%2B+I%5B4%5D+=+5100+\"$
\n" ); document.write( "========================
\n" ); document.write( "(3) $\"+I%5B1%5D+%2B+I%5B2%5D+=+4650+\"$
\n" ); document.write( "Use (1) and (2) to get:
\n" ); document.write( "(3) $\"+.05P%5B1%5D+%2B+.08P%5B2%5D+=+4650+\"$
\n" ); document.write( "---------------------------------
\n" ); document.write( "(6) $\"+I%5B3%5D+%2B+I%5B4%5D+=+5100+\"$
\n" ); document.write( "Use (4) and (5) to get:
\n" ); document.write( "(6) $\"+.08P%5B1%5D+%2B+.05P%5B2%5D+=+5100+\"$
\n" ); document.write( "---------------------------------
\n" ); document.write( "(3) $\"+5P%5B1%5D+%2B+8P%5B2%5D+=+465000+\"$
\n" ); document.write( "(6) $\"+8P%5B1%5D+%2B+5P%5B2%5D+=+510000+\"$
\n" ); document.write( "Multiply both sides of (3) by $\"+8+\"$
\n" ); document.write( "Multiply both sides of (6) by $\"+5+\"$
\n" ); document.write( "Subtract (6) from (3)
\n" ); document.write( "---------------------------------
\n" ); document.write( "(3) $\"+40P%5B1%5D+%2B+64P%5B2%5D+=+3720000+\"$
\n" ); document.write( "(6) $\"+-40P%5B1%5D+-+25P%5B2%5D+=+-2550000+\"$
\n" ); document.write( "------------------------------------
\n" ); document.write( " $\"+39P%5B2%5D+=+1170000+\"$
\n" ); document.write( " $\"+P%5B2%5D+=+30000+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+5P%5B1%5D+%2B+8P%5B2%5D+=+465000+\"$
\n" ); document.write( "(3) $\"+5P%5B1%5D+%2B+8%2A30000+=+465000+\"$
\n" ); document.write( "(3) $\"+5P%5B1%5D+=+465000+-+240000+\"$
\n" ); document.write( "(3) $\"+5P%5B1%5D+=+225000+\"$
\n" ); document.write( "(3) $\"+P%5B1%5D+=+45000+\"$
\n" ); document.write( "---------------------------------
\n" ); document.write( "P 45,000 is invested @ 5%
\n" ); document.write( "P 30,000 is invested @ 8%
\n" ); document.write( "--------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+I%5B1%5D+=+P%5B1%5D%2A.05%2A1+\"$
\n" ); document.write( "(1) $\"+I%5B1%5D+=+45000%2A.05%2A1+\"$
\n" ); document.write( "(1) $\"+I%5B1%5D+=+2250+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+I%5B2%5D+=+P%5B2%5D%2A.08%2A1+\"$
\n" ); document.write( "(2) $\"+I%5B2%5D+=+30000%2A.08%2A1+\"$
\n" ); document.write( "(2) $\"+I%5B2%5D+=+2400+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+I%5B1%5D+%2B+I%5B2%5D+=+4650+\"$
\n" ); document.write( "(3) $\"+2250+%2B+2400+=+4650+\"$
\n" ); document.write( "(3) $\"+4650+=+4650+\"$
\n" ); document.write( "OK
\n" ); document.write( "You can check $\"+I%5B3%5D+\"$ and $\"+I%5B4%5D+\"$
\n" ); document.write( "the same way\r
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\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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