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)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "x = amount invested at 5% \n" ); document.write( "9000-x = remaining amount invested at 15%\r \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "9000-x = 9000 - 8300 = 700 dollars was invested at a rate of 15%\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Answers: \n" ); document.write( "Amount invested at 5% = $8300 \n" ); document.write( "Amount invested at 15% = $700\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Check: \n" ); document.write( "8300*0.05+700*0.15 = 415 + 105 = 520 \n" ); document.write( " \n" ); document.write( " |