document.write( "Question 776043: I am not sure how to set this word problem up in order to solve.\r
\n" ); document.write( "\n" ); document.write( "Helen Weller invested $12000 in an account that pays 12% interest. How much additional money must be invested in an account that pays 11% interest so that the average rate of return on her investment is 11.667%. \n" ); document.write( "
Algebra.Com's Answer #473356 by DrBeeee(684)\"\" \"About 
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Let x = amount invested @ 11%
\n" ); document.write( "Let y = amount invested @ 12%
\n" ); document.write( "Your balance, B, is
\n" ); document.write( "(1) B = 1.11x + 1.12y
\n" ); document.write( "You want the balance to look like yoir total investment looks like it pays out at 11.667% or
\n" ); document.write( "(2) B = 1.11667*(x + y)
\n" ); document.write( "So you now equate (1) and (2) to get
\n" ); document.write( "(3) 1.11x + 1.12y = 1.11667*(x + y)
\n" ); document.write( "Now we are given that y is 12,000, so we have
\n" ); document.write( "(4) 1.11x - 1.11667x = (1.11667-1.12)*12000 or
\n" ); document.write( "(5) x = 12000*(1.12-1.11667)/(1.11667-1.11) or
\n" ); document.write( "(6) x = 5991
\n" ); document.write( "Let's check this be equating (1) and (2).
\n" ); document.write( "Is (1.11*5991+1.12*12000 = 1.11667*(5991+12000))?
\n" ); document.write( "Is (6650+13440 = 1.11667*(17991))?
\n" ); document.write( "Is (20090 = 20090)? Yes
\n" ); document.write( "Answer: Helen needs to invest $5,991 @ 11% to get the result she wants. \n" ); document.write( "
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