document.write( "Question 850724: A total of $12,000 is invested in two simple interest accounts. On one account the annual simple interest rate is 12%, on the second account the annual simple interest rate is 8%. How much should be invested in each account so that the same interest is earned on both? \n" ); document.write( "
Algebra.Com's Answer #512383 by Theo(13342)\"\" \"About 
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let x = amount invested at 12%.
\n" ); document.write( "let y = amount invested at 8%.
\n" ); document.write( "x + y = 12000
\n" ); document.write( "let i = interest earned.
\n" ); document.write( "i = .12x for amount invested at 12%.
\n" ); document.write( "i = .08y for amount invested at 8%.
\n" ); document.write( "the interest earned on each investment needs to be the same.
\n" ); document.write( "this means that:
\n" ); document.write( ".12x = .08y
\n" ); document.write( "solve for x in this equation to get:
\n" ); document.write( "x = .08y / .12 which makes x = 2/3 * y
\n" ); document.write( "in the equation of x + y = 12000, replace x with 2/3 * y to get:
\n" ); document.write( "2/3 * y + y = 12000
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "5/3 * y = 12000
\n" ); document.write( "multiply both sides of this equation by 3/5 to get:
\n" ); document.write( "y = 3/5 * 12000 which makes y = 7200.
\n" ); document.write( "since x + y = 12000, this makes x = 4800.
\n" ); document.write( "your solution should be that:
\n" ); document.write( "x = 4800 and y = 7200
\n" ); document.write( "replace x with 4800 and y with 7200 in the equation of .12x = .08y and you get:
\n" ); document.write( ".12 * 4800 = .08 * 7200
\n" ); document.write( "simplify this equation to get:
\n" ); document.write( "576 = 576
\n" ); document.write( "the interest is the same for both investments.
\n" ); document.write( "the solution is good.\r
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