document.write( "Question 991249: Leroy invested $400 at a certain interest rate and $1200 at a rate 3% higher. He earned $84 less in annual interest on the smaller investment. If the return on both investments totaled $132, find each rate. \n" ); document.write( "
Algebra.Com's Answer #611136 by Theo(13342)\"\" \"About 
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let x equal the certain interest rate that 400 is invested at.
\n" ); document.write( "let x + .03 equal the interest rate that 1200 is invested at.
\n" ); document.write( "why .03?
\n" ); document.write( "because the decimal equivalent of 3% is equal to .03.
\n" ); document.write( "your formula becomes:
\n" ); document.write( "x * 400 + (x + .03) * 1200 = 132
\n" ); document.write( "you are also told that the interest on the smaller investment is 84 dollars less than the interest on the larger investment.
\n" ); document.write( "this means that:
\n" ); document.write( "400 * x = 1200 * (x + .03) - 84
\n" ); document.write( "in your original formula of x * 400 + (x + .03) * 1200 = 132,
\n" ); document.write( "you can replace 400 * x with 1200 * (x + .03) - 84 because they are equal to each other.
\n" ); document.write( "your formula becomes:
\n" ); document.write( "1200 * (x + .03) - 84 + 1200 * (x + .03) = 132
\n" ); document.write( "add 84 to both sides of that equation to get:
\n" ); document.write( "1200 * (x + .03) + 1200 * (x + .03) = 216
\n" ); document.write( "simplify this formula to get:
\n" ); document.write( "2400 * (x + .03) = 216
\n" ); document.write( "divide both sides of this formula to get:
\n" ); document.write( "x + .03 = 216 / 2400 = .09
\n" ); document.write( "solve for x to get x = .06
\n" ); document.write( "you have:
\n" ); document.write( "x = .06
\n" ); document.write( "x + .03 = .09
\n" ); document.write( "your original formula of x * 400 + (x + .03) * 1200 = 132 becomes:
\n" ); document.write( ".06 * 400 + .09 * 1200 = 132
\n" ); document.write( "evaluate this equation to get:
\n" ); document.write( "24 + 108 = 132
\n" ); document.write( "simplify to get:
\n" ); document.write( "132 = 132
\n" ); document.write( "problem is solved.
\n" ); document.write( "interest rate of the smaller investment is 6%.
\n" ); document.write( "interest rate of the larger investment is 9%.\r
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