document.write( "Question 1195905: A total of $9000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $520? \n" ); document.write( "
Algebra.Com's Answer #828527 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "x = amount invested at 5%
\n" ); document.write( "9000-x = remaining amount invested at 15%\r
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\n" ); document.write( "\n" ); document.write( "Assuming simple interest is involved (instead of compound interest), we then use this formula
\n" ); document.write( "i = P*r*t
\n" ); document.write( "where,
\n" ); document.write( "P = principal aka deposit
\n" ); document.write( "r = interest rate in decimal form
\n" ); document.write( "t = number of years\r
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\n" ); document.write( "\n" ); document.write( "The portion invested at 5% will get us this amount of interest
\n" ); document.write( "i = P*r*t
\n" ); document.write( "i = x*0.05*1
\n" ); document.write( "i = 0.05x
\n" ); document.write( "which is what we'll have at the end of the year from this one investment.\r
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\n" ); document.write( "\n" ); document.write( "The other account yields...
\n" ); document.write( "i = P*r*t
\n" ); document.write( "i = (9000-x)*0.15*1
\n" ); document.write( "i = 1350-0.15x\r
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\n" ); document.write( "\n" ); document.write( "These two interest subtotals add to the stated annual interest of $520
\n" ); document.write( "(0.05x) + (1350-0.15x) = 520
\n" ); document.write( "-0.10x + 1350 = 520
\n" ); document.write( "-0.10x = 520-1350
\n" ); document.write( "-0.10x = -830
\n" ); document.write( "x = -830/(-0.10)
\n" ); document.write( "x = 8300 dollars was invested at a 5% interest rate\r
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\n" ); document.write( "\n" ); document.write( "9000-x = 9000 - 8300 = 700 dollars was invested at a rate of 15%\r
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\n" ); document.write( "\n" ); document.write( "Answers:
\n" ); document.write( "Amount invested at 5% = $8300
\n" ); document.write( "Amount invested at 15% = $700\r
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\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "8300*0.05+700*0.15 = 415 + 105 = 520
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