SOLUTION: 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 tot

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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.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x equal the certain interest rate that 400 is invested at.
let x + .03 equal the interest rate that 1200 is invested at.
why .03?
because the decimal equivalent of 3% is equal to .03.
your formula becomes:
x * 400 + (x + .03) * 1200 = 132
you are also told that the interest on the smaller investment is 84 dollars less than the interest on the larger investment.
this means that:
400 * x = 1200 * (x + .03) - 84
in your original formula of x * 400 + (x + .03) * 1200 = 132,
you can replace 400 * x with 1200 * (x + .03) - 84 because they are equal to each other.
your formula becomes:
1200 * (x + .03) - 84 + 1200 * (x + .03) = 132
add 84 to both sides of that equation to get:
1200 * (x + .03) + 1200 * (x + .03) = 216
simplify this formula to get:
2400 * (x + .03) = 216
divide both sides of this formula to get:
x + .03 = 216 / 2400 = .09
solve for x to get x = .06
you have:
x = .06
x + .03 = .09
your original formula of x * 400 + (x + .03) * 1200 = 132 becomes:
.06 * 400 + .09 * 1200 = 132
evaluate this equation to get:
24 + 108 = 132
simplify to get:
132 = 132
problem is solved.
interest rate of the smaller investment is 6%.
interest rate of the larger investment is 9%.