document.write( "Question 659032: $27,090 is invested, part at 13% and the rest at 10%. If the interest earned from the amount invested at 13% exceeds the interest earned from the amount invested at 10% by $440.16, how much is invested at each rate? (Round to two decimal places if necessary.\r
\n" ); document.write( "\n" ); document.write( "I've tried to work out this problem 2 different ways! Still, I have no luck. Please Help! \n" ); document.write( "
Algebra.Com's Answer #410604 by Theo(13342)\"\" \"About 
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27090 is invested.
\n" ); document.write( "part at 13%
\n" ); document.write( "part at 10%
\n" ); document.write( "the interest earned at 13% exceeds the interest earned at 10% by 440.16
\n" ); document.write( "how much is invested at each rate.
\n" ); document.write( "let x = the amount of money invested at 13%
\n" ); document.write( "let y = the amount of money invested at 10%
\n" ); document.write( "so far you get 2 equations.
\n" ); document.write( "x + y = 27090
\n" ); document.write( ".13x + .10y = total interest earned.
\n" ); document.write( "unfortunately we don't know that, but we do know that .13x - .10y = 440.16
\n" ); document.write( "we should be able to used that equation to solve for x and y.
\n" ); document.write( "we have 2 equations that need to be solved simultaneously
\n" ); document.write( "they are:
\n" ); document.write( "x + y = 27090
\n" ); document.write( ".13x - .10y = 440.16
\n" ); document.write( "if we multiply both sides of the top equation by .10, then that equation becomes:
\n" ); document.write( ".10x + .10y = 2709
\n" ); document.write( "our 2 equations are now:
\n" ); document.write( ".10x + .10y = 2709.00
\n" ); document.write( ".13x - .10y = 440.16
\n" ); document.write( "if we add these equations together we will get:
\n" ); document.write( ".23x = 3149.16
\n" ); document.write( "if we divide both equations by 23 we will get:
\n" ); document.write( "x = 13692
\n" ); document.write( "this means that y must be equal to 27090 - 13692 = 13398
\n" ); document.write( "we have:
\n" ); document.write( "x = 13692
\n" ); document.write( "y = 13398
\n" ); document.write( ".13x = .13 * 13692 = 1779.96
\n" ); document.write( ".10y = .10 * 13398 = 1339.8
\n" ); document.write( ".13x - .10y = 440.16
\n" ); document.write( "this looks to be a good answer.
\n" ); document.write( "13,692 is invested at 13%
\n" ); document.write( "13,398 is invested at 10%
\n" ); document.write( "the simultaneous equations could also have been solved by substitution as follows:
\n" ); document.write( "start with:
\n" ); document.write( "x + y = 27090
\n" ); document.write( ".13x - .10y = 440.16
\n" ); document.write( "solve for y in the first equation to get:
\n" ); document.write( "y = 27090 - x
\n" ); document.write( "substitute for y in the second equation to get:
\n" ); document.write( ".13x - .10(27090-x) = 440.16
\n" ); document.write( "simplify to get:
\n" ); document.write( ".13x - .10*27090 + .10x = 440.16
\n" ); document.write( "simplify further to get:
\n" ); document.write( ".13x - 2709 + .10x = 440.16
\n" ); document.write( "combine like terms to get .23x - 2709 = 440.16
\n" ); document.write( "add 2709 to both sides of the equation to get:
\n" ); document.write( ".23x = 3149.16
\n" ); document.write( "divide both sides by .23 to get:
\n" ); document.write( "x = 13692
\n" ); document.write( "you get the same value for x which leads to the same value for y so both methods (elimination method was used first) give you the same result as they should.\r
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