document.write( "Question 624588: You have already invested $450 in a stock with an annual return of 11%. How much of an additional $800 should be invested at 12% and how much at 6% so that the total return on the entire $1,250 is 9%? (Round each answer to the nearest cent.) \n" ); document.write( "
Algebra.Com's Answer #392945 by Theo(13342)\"\" \"About 
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original investment = 450 with annual return of 11%.
\n" ); document.write( "add $800, some at 12% and some at 6%.
\n" ); document.write( "total return on entire $1250 equals 9%.
\n" ); document.write( "assume x at 12% and assume 800-x at 6%
\n" ); document.write( "sum of all investment is equal to 800 + 450 = 1250
\n" ); document.write( "total interest = 1250 * .09
\n" ); document.write( "your formula is:
\n" ); document.write( ".11*450 + .12*x + .06(800-x) = .09*1250
\n" ); document.write( "simplify to get:
\n" ); document.write( ".11*450 + .12*x + .06*800 - .06*x = .09*1250
\n" ); document.write( "simplify further to get:
\n" ); document.write( "49.5 + .12*x + 48 - .06*x = 112.5
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "97.5 + .06*x = 112.5
\n" ); document.write( "subtract 97.5 from both sides of the equation to get:
\n" ); document.write( ".06*x = 112.5 - 97.5 which simplifies to:
\n" ); document.write( ".06*x = 15
\n" ); document.write( "divide both sides by .06 to get:
\n" ); document.write( "x = 15/.06 which simplifies to:
\n" ); document.write( "x = 250
\n" ); document.write( "when x = 250, 800 - x = 550
\n" ); document.write( "your formula of:
\n" ); document.write( ".11*450 + .12*x + .06(800-x) = .09*1250 becomes:
\n" ); document.write( ".11*450 + .12*250 + .06*550 = .09*1250 which simplifies to:
\n" ); document.write( "49.5 + 30 + 33 = 112.5
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "112.5 = 112.5
\n" ); document.write( "this confirms the results of x = 250 and 800-x = 550 as good.
\n" ); document.write( "you need to invest 450 at 11% and 250 at 12% and 550 at 6% and you'll get a total combined interest rate of .09 on the total of 1250.\r
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